Optical measurement apparatus and optical measurement method

ABSTRACT

An optical measurement method with an optical measurement apparatus including an irradiation optical system and a measurement optical system is provided. The optical measurement method includes obtaining a distribution of actually measured values when angles of incidence are different for the same sample, calculating a modification factor depending on an angle of incidence on the measurement optical system from each measurement point in association with a region in the two-dimensional image corresponding to each measurement point in the measurement target irradiated with the measurement light, and calculating optical characteristics including a refractive index of the sample based on a group of pixel values in one row or a plurality of rows along any one direction in the distribution of the actually measured values and a corresponding modification factor.

BACKGROUND OF THE INVENTION Field of the Invention

The present technical concept relates to an optical measurementapparatus and an optical measurement method capable of measuring opticalcharacteristics such as a film thickness and a refractive index.

Description of the Background Art

A technique to measure a film thickness of a sample such as a functionalresin film or a semiconductor substrate has been known. For example,Japanese Patent Laying-Open No. 2009-092454 discloses a multi-layeredfilm analysis apparatus and a multi-layered film analysis method capableof highly accurately measuring a film thickness of a multi-layered filmsample having wavelength-dependency. Japanese Patent Laying-Open No.2013-079921 discloses a film thickness measurement apparatus and a filmthickness measurement method capable of accurately measuring a thicknessof a dielectric thin film of which refractive index is not known.

In general, a sample to be subjected to measurement has a certain area,and there is a need for quick measurement of a film thicknessdistribution (an in-plane film thickness distribution) at a surface tobe subjected to measurement. In order to meet such needs, JapanesePatent Laying-Open No. 2004-279296 discloses an approach for quicklyobtaining a thickness distribution of a formed thin film with asimplified apparatus configuration in forming a thin film on a flatplate in a process for manufacturing a liquid crystal display. Morespecifically, Japanese Patent Laying-Open No. 2004-279296 discloses amethod of allowing light emitted from a light source to enter a coatingprovided on a substrate to be subjected to measurement, measuring lightreflected from the coating which has caused interference with a lightreception apparatus with an angle of incidence of the light emitted to amain surface of the coating being varied stepwise, and obtaining athickness of the coating based on the angle of incidence of the emittedlight which takes a relative maximum value and a relative minimum valuein variation in intensity of reception of measured reflected light.

With increase in size of a sample, there is a need for measurement of anin-plane film thickness distribution of a larger sample at a higherspeed and with higher accuracy. The configurations disclosed in JapanesePatent Laying-Open No. 2009-092454 and Japanese Patent Laying-Open No.2013-079921 are basically directed to measurement by irradiation withlight to one certain point of a sample, and they are unable tosufficiently meet the need for quick measurement of an in-plane filmthickness distribution.

Japanese Patent Laying-Open No. 2004-279296 adopts what is called apeak-valley method of calculating a film thickness by using positionswhere a relative maximum value and a relative minimum value of aninterference waveform are produced. With the peak-valley method, a filmthickness may not accurately be measured under the influence by noiseoriginating from an optical system. In addition, with the peak-valleymethod, a thickness of each layer of a sample in which a plurality oflayers are stacked cannot be measured. Therefore, though Japanese PatentLaying-Open No. 2004-279296 may be applicable to a process formanufacturing a liquid crystal display, it is unable to measure anin-plane film thickness distribution of various samples in general.

SUMMARY OF THE INVENTION

One object of the present technical concept is to provide an opticalmeasurement apparatus and an optical measurement method capable ofmeasuring an in-plane film thickness distribution of various samples ata higher speed and with higher accuracy. Another object of the presenttechnical concept is to provide an optical measurement apparatus and anoptical measurement method capable of measuring optical characteristicsof a sample such as a refractive index without using a dedicatedmeasurement apparatus.

An optical measurement apparatus according to one embodiment includes anirradiation optical system configured to linearly irradiate ameasurement target with measurement light having a certain wavelengthrange, a measurement optical system which receives linear measurementinterference light which is transmitted light or reflected lightoriginating from the measurement target as a result of irradiation withthe measurement light, and a processing device. The measurement opticalsystem includes a diffraction grating which expands the measurementinterference light in a wavelength direction orthogonal to alongitudinal direction of the measurement interference light and animaging portion which outputs a two-dimensional image by receiving themeasurement interference light expanded in the wavelength direction bythe diffraction grating. The processing device includes a firstcalculation module that calculates a modification factor depending on anangle of incidence on the measurement optical system from eachmeasurement point in association with a region in the two-dimensionalimage corresponding to each measurement point in the measurement targetirradiated with the measurement light and a second calculation modulethat calculates optical characteristics of the measurement target byapplying a corresponding modification factor to each pixel valueincluded in the two-dimensional image.

The modification factor may include a wave number representing aparameter including a wavelength of the measurement light and arefractive index of the measurement target. The wave number iscalculated in consideration of magnitude of a corresponding angle ofincidence, for each pixel position in the two-dimensional image.

The second calculation module may subject a row of values resulting fromconversion in accordance with a relational expression for linearizingthe pixel value of the two-dimensional image corresponding to ameasurement point of interest with respect to a phase factor, to Fouriertransform with respect to a row of corresponding wave numbers, determinea film thickness at the measurement point of interest based on a peakposition which appears in a power spectrum obtained through Fouriertransform, and aggregate film thicknesses determined for a plurality ofmeasurement points and outputting the resultant aggregate as a filmthickness distribution.

The wave number may be calculated in consideration ofwavelength-dependency of a refractive index of the measurement target.

The modification factor may include a value representing magnitude of anangle of incidence corresponding to each measurement point. The secondcalculation module may adopt a film thickness at each measurement pointas a fluctuating parameter and calculate a theoretical value of eachpixel corresponding to the two-dimensional image based on a refractiveindex of the measurement target, a value representing magnitude of theangle of incidence corresponding to each measurement point, andcorrespondence between each measurement point and a pixel position inthe two-dimensional image and determine a film thickness at eachmeasurement point by adjusting the fluctuating parameter such that asimilarity between the calculated theoretical value of each pixel andeach pixel value of the two-dimensional image is higher.

An optical measurement method according to another embodiment includeslinearly irradiating a measurement target with measurement light havinga certain wavelength range and receiving linear measurement interferencelight which is transmitted light or reflected light originating from themeasurement target as a result of irradiation with the measurementlight, expanding the measurement interference light in a wavelengthdirection orthogonal to a longitudinal direction of the measurementinterference light and outputting a two-dimensional image by receivingthe measurement interference light expanded in the wavelength direction,calculating a modification factor depending on an angle of incidencefrom each measurement point in association with a region in thetwo-dimensional image corresponding to each measurement point in themeasurement target irradiated with the measurement light, andcalculating optical characteristics of the measurement target byapplying a corresponding modification factor to each pixel valueincluded in the two-dimensional image.

The modification factor may include a wave number representing aparameter including a wavelength of the measurement light and arefractive index of the measurement target. The wave number may becalculated in consideration of magnitude of a corresponding angle ofincidence, for each pixel position in the two-dimensional image.

The calculating optical characteristics may include subjecting a row ofvalues resulting from conversion in accordance with a relationalexpression for linearizing the pixel value of the two-dimensional imagecorresponding to a measurement point of interest with respect to a phasefactor, to Fourier transform with respect to a row of corresponding wavenumbers, determining a film thickness at the measurement point ofinterest based on a peak position which appears in a power spectrumobtained through Fourier transform, and aggregating film thicknessesdetermined for a plurality of measurement points and outputting theresultant aggregate as a film thickness distribution.

The wave number may be calculated in consideration ofwavelength-dependency of a refractive index of the measurement target.

The modification factor may include a value representing magnitude of anangle of incidence corresponding to each measurement point. Thecalculating optical characteristics may include adopting a filmthickness at each measurement point as a fluctuating parameter andcalculating a theoretical value of each pixel corresponding to thetwo-dimensional image based on a refractive index of the measurementtarget, a value representing magnitude of the angle of incidencecorresponding to each measurement point, and correspondence between eachmeasurement point and a pixel position in the two-dimensional image anddetermining a film thickness at each measurement point by adjusting thefluctuating parameter such that a similarity between the calculatedtheoretical value of each pixel and each pixel value of thetwo-dimensional image is higher.

According to yet another embodiment, an optical measurement method withan optical measurement apparatus including an irradiation optical systemand a measurement optical system is provided, the irradiation opticalsystem being configured to linearly irradiate a measurement target withmeasurement light having a certain wavelength range, the measurementoptical system being configured to output a two-dimensional image byexpanding linear measurement interference light in a wavelengthdirection orthogonal to a longitudinal direction of the measurementinterference light, the measurement interference light being transmittedlight or reflected light originating from the measurement target as aresult of irradiation with the measurement light. The opticalmeasurement method includes obtaining a distribution of actuallymeasured values when angles of incidence are different for the samesample, calculating a modification factor depending on an angle ofincidence on the measurement optical system from each measurement pointin association with a region in the two-dimensional image correspondingto each measurement point in the measurement target irradiated with themeasurement light, and calculating optical characteristics including arefractive index of the sample based on a group of pixel values in onerow or a plurality of rows along any one direction in the distributionof the actually measured values and corresponding modification factors.

The calculating optical characteristics may include calculating filmthicknesses at a plurality of positions in the distribution of theactually measured values based on a set refractive index, a modificationfactor corresponding to each position, and a group of pixel values in awavelength direction at each position, calculating a film thicknessdispersion which is a dispersion for the calculated film thicknesses,repeating the calculating film thicknesses and the calculating a filmthickness dispersion, with the refractive index of the sample being setto a plurality of different values, and determining a refractive indexof the sample based on the calculated film thickness dispersion.

The determining a refractive index of the sample may include determininga refractive index at which the calculated film thickness dispersionbecomes small as a refractive index of the sample.

The determining a refractive index of the sample may include fitting apolynomial representing a predetermined film thickness dispersion torelation between a refractive index and a film thickness dispersion anddetermining a refractive index of the sample based on a point at whichthe film thickness dispersion represented by the polynomial determinedby fitting takes an extreme value.

The determining a refractive index of the sample may include fitting apolynomial representing a predetermined squared residual value torelation between a refractive index and a squared residual value for thecalculated film thicknesses and determining a refractive index of thesample based on a point at which the squared residual value representedby the polynomial determined by fitting takes an extreme value.

A refractive index of the sample may be calculated in accordance with aprescribed wavelength dispersion formula. The determining a refractiveindex of the sample may include applying a least squares method to anyof relation between each coefficient defining the wavelength dispersionformula and a film thickness dispersion and relation between eachcoefficient defining the wavelength dispersion formula and a squaredresidual value and determining a refractive index of the sample based ona set of coefficients at the time when the film thickness dispersion orthe squared residual value takes an extreme value.

The calculating optical characteristics may include calculating adistribution of actually measured values exhibited by a group of pixelvalues in a position direction for any wavelength in the distribution ofthe actually measured values, calculating a distribution of theoreticalvalues for any wavelength based on a film thickness and a refractiveindex of the sample that are set in advance and a modification factorcorresponding to each position, and determining a film thickness and arefractive index of the sample so as to decrease an error between thedistribution of the theoretical values and the distribution of theactually measured values.

The calculating optical characteristics may include determining arefractive index of the sample for each of a plurality of wavelengths inthe distribution of the actually measured values.

The calculating optical characteristics may include calculating filmthicknesses of the sample for a plurality of wavelengths in thedistribution of the actually measured values based on the error betweenthe distribution of the theoretical values and the distribution of theactually measured values and determining a more probable film thicknessbased on the calculated film thicknesses.

The refractive index of the sample used for calculation of thedistribution of the theoretical values may be calculated in accordancewith a prescribed wavelength dispersion formula. The calculating opticalcharacteristics may include fitting each coefficient defining theprescribed wavelength dispersion formula and the film thickness so as todecrease errors between the distribution of the theoretical values andthe distribution of the actually measured values for a plurality ofwavelengths in the distribution of the actually measured values.

An optical measurement apparatus according to still another embodimentincludes an irradiation optical system configured to linearly irradiatea measurement target with measurement light having a certain wavelengthrange, a measurement optical system configured to output atwo-dimensional image by expanding linear measurement interference lightin a wavelength direction orthogonal to a longitudinal direction of themeasurement interference light, the measurement interference light beingtransmitted light or reflected light originating from the measurementtarget as a result of irradiation with the measurement light, and aprocessing device. The processing device may obtain a distribution ofactually measured values when angles of incidence are different for thesame sample, calculate a modification factor depending on an angle ofincidence on the measurement optical system from each measurement pointin association with a region in the two-dimensional image correspondingto each measurement point in the measurement target irradiated with themeasurement light, and calculate optical characteristics including arefractive index of the sample based on a group of pixel values in onerow or a plurality of rows along any one direction in the distributionof the actually measured values and corresponding modification factors.

The foregoing and other objects, features, aspects and advantages of thepresent invention will become more apparent from the following detaileddescription of the present invention when taken in conjunction with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing a schematic configuration of atransmissive optical measurement apparatus according to the presentembodiment.

FIG. 2 is a schematic diagram showing a schematic configuration of areflective optical measurement apparatus according to the presentembodiment.

FIG. 3 is a schematic diagram showing a schematic configuration of ameasurement optical system adopted in the optical measurement apparatusaccording to the present embodiment.

FIG. 4 is a schematic diagram showing a schematic configuration of aposition adjustment mechanism adopted in the optical measurementapparatus according to the present embodiment.

FIG. 5 is a schematic diagram showing a schematic configuration of aprocessing device according to the present embodiment.

FIG. 6 is a diagram for illustrating incidence of measurementinterference light on the measurement optical system of the opticalmeasurement apparatus according to the present embodiment.

FIGS. 7A and 7B are diagrams for illustrating principles of a filmthickness measurement method according to the present embodiment.

FIGS. 8A and 8B are diagrams showing examples of a two-dimensional imagehandled in the optical measurement apparatus according to the presentembodiment.

FIG. 9 is a diagram for illustrating binning processing in calculatingan angle of incidence used in the film thickness measurement methodaccording to the present embodiment.

FIG. 10 is a diagram for illustrating a method of calculating an angleof incidence used in the film thickness measurement method according tothe present embodiment.

FIG. 11 is a flowchart showing a processing procedure (No. 1) in thefilm thickness measurement method according to the present embodiment.

FIG. 12 is a diagram for illustrating processing contents in theprocessing procedure (No. 1) in the film thickness measurement methodshown in FIG. 11.

FIG. 13 is a diagram showing one example of a wavelength distribution ofa refractive index of a polyethylene thin film.

FIG. 14 is a diagram showing one example of a film thickness trendobtained with the film thickness measurement method according to thepresent embodiment.

FIG. 15 is a diagram showing one example of a two-dimensional imageexhibiting a transmittance spectrum in accordance with a theoreticalformula according to the present embodiment.

FIG. 16 is a graph showing a transmittance spectrum T(λ) correspondingto a position-direction pixel number j in the two-dimensional image(theoretical value) shown in FIG. 15.

FIGS. 17A and 17B are graphs showing a wave-number-convertedtransmittance T′(K₁) calculated from transmittance spectrum T(λ) shownin FIG. 16.

FIG. 18 is a diagram showing one example of a film thickness trendcalculated from wave-number-converted transmittance T′(K₁) shown inFIGS. 17A and 17B.

FIG. 19 is a schematic diagram for illustrating processing contents in aprocessing procedure (No. 2) in the film thickness measurement methodaccording to the present embodiment.

FIG. 20 is a flowchart showing the processing procedure (No. 2) in thefilm thickness measurement method according to the present embodiment.

FIGS. 21 and 22 are schematic diagrams for illustrating overview of arefractive index measurement method according to the present embodiment.

FIGS. 23A and 23B are graphs showing examples of a film thickness trendcalculated in accordance with a refractive index measurement method(No. 1) based on information in a wavelength direction according to thepresent embodiment.

FIG. 24 is a flowchart showing a processing procedure in the refractiveindex measurement method (No. 1) based on information in the wavelengthdirection according to the present embodiment.

FIG. 25 is a diagram for illustrating a method of determining arefractive index in the refractive index measurement method (No. 2)based on information in the wavelength direction according to thepresent embodiment.

FIG. 26 is a diagram for illustrating a method of determining arefractive index in the refractive index measurement method (No. 3)based on information in the wavelength direction according to thepresent embodiment.

FIG. 27 is a diagram for illustrating a method of determining a moreprobable value of a film thickness in the refractive index measurementmethod (No. 2) based on information in a position direction according tothe present embodiment.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

An embodiment of the present invention will be described in detail withreference to the drawings. The same or corresponding elements in thedrawings have the same reference characters allotted and descriptionthereof will not be repeated.

A. Apparatus Configuration of Optical Measurement Apparatus

An apparatus configuration of an optical measurement apparatus accordingto the present embodiment will initially be described. The opticalmeasurement apparatus according to the present embodiment is ameasurement apparatus with an imaging spectroscope, and obtainswavelength information at each measurement point on a measurement lineirradiated with measurement light by irradiating a measurement target(which is also referred to as a “sample” below) with linear measurementlight and splitting light resulting from passage of the linearmeasurement light through the sample or reflected light resulting fromreflection of the linear measurement light by the sample. Sincetransmitted light or reflected light originating from the sampleexhibits results from occurrence of interference in the sample, it isalso referred to as “measurement interference light” below.

A typical apparatus configuration of the optical measurement apparatusaccording to the present embodiment will be shown below.

(a1: Transmissive System)

FIG. 1 is a schematic diagram showing a schematic configuration of atransmissive optical measurement apparatus 1 according to the presentembodiment. Referring to FIG. 1, optical measurement apparatus 1includes a measurement optical system 10, a light source 20 configuredto generate measurement light, a linear light guide 22 configured toirradiate a sample S with measurement light generated by light source20, and a processing device 100.

Light source 20 and linear light guide 22 correspond to a linear lightsource unit (an irradiation optical system) which linearly irradiatessample S with light having a certain wavelength range. A wavelengthrange of the measurement light is determined by a range of wavelengthinformation to be obtained from sample S. For example, a halogen lamp isemployed as light source 20.

Linear light guide 22 is typically arranged directly under a surfacewhere sample S is transported and irradiates sample S with measurementlight from light source 20 through a linear opening. A diffusion memberfor suppressing unevenness in quantity of light is arranged on anirradiation surface of linear light guide 22. Measurement light fromlinear light guide 22 is incident on sample S, and a measurement line 24irradiated with measurement light is produced.

Measurement optical system 10 receives linear measurement interferencelight which is transmitted light or reflected light originating fromsample S as a result of irradiation with measurement light. Morespecifically, measurement optical system 10 obtains wavelengthdistribution characteristics of a transmittance or a reflectance at eachmeasurement point based on measurement interference light which haspassed through sample S or measurement interference light reflected bysample S. Measurement optical system 10 is arranged at a positionopposed to linear light guide 22 with sample S lying therebetween. Lightwhich has passed through sample S (measurement interference light) ofmeasurement light irradiated from linear light guide 22 is incident onmeasurement optical system 10. Measurement optical system 10 is fixed bya base member 4 and a support member 6.

Measurement optical system 10 includes an object lens 12, an imagingspectroscope 14, and an imaging portion 16. Transmitted light fromsample S is converged by object lens 12 and guided to imagingspectroscope 14.

Imaging spectroscope 14 collectively measures spectroscopic informationat each measurement point on a line of sample S. More specifically,imaging spectroscope 14 expands incident linear transmitted light in awavelength direction and outputs the expanded light to imaging portion16. Imaging portion 16 is implemented by an imaging device having atwo-dimensional light reception surface. Such an imaging device isimplemented, for example, by a charge coupled device (CCD) image sensoror a complementary metal oxide semiconductor (CMOS) image sensor.Imaging portion 16 outputs a two-dimensional image by receivingtransmitted light from imaging spectroscope 14 at the imaging device.The output two-dimensional image includes wavelength information andposition information. Details of measurement optical system 10 will bedescribed later.

Processing device 100 calculates a characteristic value of sample S suchas a film thickness at each measurement point on measurement line 24 byperforming processing as will be described later on the two-dimensionalimage output from measurement optical system 10 (imaging portion 16).Details of measurement processing by processing device 100 will bedescribed later.

(a2: Reflective System)

FIG. 2 is a schematic diagram showing a schematic configuration of areflective optical measurement apparatus 2 according to the presentembodiment. Referring to FIG. 2, optical measurement apparatus 2 isdifferent from optical measurement apparatus 1 in positional relation ofmeasurement optical system 10 and linear light guide 22. Specifically,linear light guide 22 is arranged such that measurement light to sampleS forms an angle of incidence Θ (>0) with respect to a surface includingmeasurement line 24 and a vertical direction 28. Measurement opticalsystem 10 is arranged at a position where it can receive light resultingfrom reflection of measurement light incident on sample S (measurementinterference light). Measurement optical system 10 is arranged such thatan optical axis thereof forms the same angle of incidence Θ with respectto the surface including measurement line 24 and vertical direction 28.

Since optical measurement apparatus 2 is otherwise substantially thesame in configuration as optical measurement apparatus 1, detaileddescription will not be repeated.

For the sake of convenience of description, details will be describedbasically with reference to optical measurement apparatus 1 which adoptsthe transmissive system.

(a3: Measurement Optical System)

Measurement optical system 10 adopted in the optical measurementapparatus according to the present embodiment will now be described.

FIG. 3 is a schematic diagram showing a schematic configuration ofmeasurement optical system 10 adopted in the optical measurementapparatus according to the present embodiment. Referring to FIG. 3, inmeasurement optical system 10, measurement interference light fromsample S is incident on imaging spectroscope 14 after it forms an imageon object lens 12.

Imaging spectroscope 14 includes a slit 142, a first lens 144, adiffraction grating 146, and a second lens 148 in the order of proximityto sample S.

Slit 142 shapes a cross-section of a beam of measurement interferencelight incident on object lens 12 into a prescribed shape. A length ofslit 142 in a longitudinal direction is set to a length in accordancewith measurement line 24 produced on sample S, and a width of slit 142in a direction of a short side is set in accordance with a resolution ofdiffraction grating 146.

First lens 144 is typically implemented by a collimating lens, and itconverts measurement interference light which has passed through slit142 into parallel light and guides the parallel light to diffractiongrating 146.

Diffraction grating 146 expands measurement interference light in awavelength direction orthogonal to the longitudinal direction ofmeasurement interference light. More specifically, diffraction grating146 expands linear measurement interference light which has passedthrough object lens 12 and slit 142 in the wavelength directionorthogonal to a line direction. As a result of wavelength expansion bydiffraction grating 146, a two-dimensional image 150 corresponding tothe longitudinal direction of measurement line 24 and the directionorthogonal to the longitudinal direction is created on a light receptionsurface of an imaging device 160 of imaging portion 16. Imaging portion16 outputs a two-dimensional image by receiving the measurementinterference light which has been expanded by diffraction grating 146 inthe wavelength direction. Though FIG. 3 shows an example in which atransmission diffraction grating is adopted as diffraction grating 146,a reflection diffraction grating may be adopted.

In the description below, a direction of two-dimensional image 150corresponding to the longitudinal direction of measurement line 24 onsample S is referred to as a “position direction” and a direction ofwavelength expansion orthogonal to the position direction is referred toas a “wavelength direction.” Each point in the position directioncorresponds to each measurement point on measurement line 24 and eachpoint in the wavelength direction corresponds to each wavelength at acorresponding measurement point.

As shown in FIG. 3, measurement optical system 10 linearly takes inmeasurement interference light from sample S through object lens 12 andslit 142. Linear measurement interference light is converted to parallellight by first lens 144, and transmission or reflection diffractiongrating 146 arranged in a stage subsequent to first lens 144 expands thelinear measurement interference light in the direction orthogonal to theposition direction (wavelength direction) (i.e., splits the linearmeasurement interference light). Second lens 148 arranged in asubsequent stage forms an image of the measurement interference lightsubjected to wavelength expansion as a two-dimensional optical spectrumwhich reflects wavelength information and position information.Two-dimensional imaging device 160 receives light of a formed image.

In the description below, the light reception surface of imaging device160 has C_(x) channels as a resolution in the wavelength direction andC_(y) channels as a resolution in the position direction.

As described above, two-dimensional image 150 reflects wavelengthinformation and position information. By using such a two-dimensionalimage 150, wavelength information at a plurality of measurement pointsset in sample S can collectively be obtained.

(a4: Position Adjustment Mechanism of Measurement Optical System)

A position adjustment mechanism of measurement optical system 10 whichcan be mounted on the optical measurement apparatus according to thepresent embodiment will now be described. In order to appropriatelyguide measurement interference light which has passed through sample Sor measurement interference light reflected by sample S to measurementoptical system 10, a position of measurement optical system 10 withrespect to sample S should appropriately be adjusted. Some of suchposition adjustment mechanisms of measurement optical system 10 andposition adjustment methods with the position adjustment mechanism willbe described below.

FIG. 4 is a schematic diagram showing a schematic configuration of aposition adjustment mechanism 170 adopted in the optical measurementapparatus according to the present embodiment. Position adjustmentmechanism 170 shown in FIG. 4 is arranged between slit 142 and firstlens 144. Position adjustment mechanism 170 includes a shutter 172 and alight source 174 which generates observation light. Observation light islight for adjustment of a position of a focus of measurement opticalsystem 10 on sample S and adjustment of a position of observation ofmeasurement optical system 10 with respect to sample S.

Shutter 172 is arranged at an intersection of an optical axis of slit142 and first lens 144 and an optical axis of light source 174. Shutter172 can make transition between an opened state and a closed state. Inthe opened state, shutter 172 allows passage of light from slit 142toward first lens 144. In the closed state, shutter 172 cuts off anoptical path from slit 142 toward first lens 144 and a mirror attachedto a rear surface of shutter 172 reflects observation light from lightsource 174 toward slit 142. When shutter 172 is closed, sample S isirradiated with observation light from light source 174.

A user can appropriately adjust a distance (a position of a focus) fromsample S to measurement optical system 10 by adjusting a position ofmeasurement optical system 10 while the user views a state ofobservation light which appears on sample S, and can appropriatelyadjust a position on sample S observed by measurement optical system 10(a position of a measurement site). By turning on light source 174,closing shutter 172, and adjusting a position of measurement opticalsystem 10 or focus of object lens 12 so as to maximize a contrast ofobservation light which appears on sample S, a portion of measurement bymeasurement optical system 10 can be checked and focusing of measurementoptical system 10 can be achieved.

In another method of adjusting a position of measurement optical system10, a position of measurement optical system 10 may be adjusted byarranging a test chart instead of sample S and evaluatingtwo-dimensional image 150 obtained by imaging the test chart withimaging portion 16. For example, a pattern such as the Ronchi ruling ormonochrome stripes at regular intervals can be employed as the testchart. When such a pattern is used, a distance (a position of a focus)from sample S to measurement optical system 10 may be adjusted tomaximize a ratio of contrast shown in actually imaged two-dimensionalimage 150.

B. Device Configuration of Processing Device

A device configuration of processing device 100 included in the opticalmeasurement apparatus according to the present embodiment will now bedescribed. Processing device 100 according to the present embodiment istypically implemented by a general-purpose computer.

FIG. 5 is a schematic diagram showing a schematic configuration ofprocessing device 100 according to the present embodiment. Referring toFIG. 5, processing device 100 includes a processor 102, a main memory104, an input portion 106, a display 108, a storage 110, a communicationinterface 120, a network interface 122, and a medium drive 124.

Processor 102 is typically an operational processing unit such as acentral processing unit (CPU) and a graphics processing unit (GPU) andexecutes one program or a plurality of programs stored in storage 110 byreading the same into main memory 104.

Main memory 104 is a volatile memory such as a dynamic random accessmemory (DRAM) or a static random access memory (SRAM) and functions as aworking memory for processor 102 to execute a program.

Input portion 106 includes a keyboard and/or a mouse and accepts anoperation by a user. Display 108 outputs a result of execution of aprogram by processor 102 to the user.

Storage 110 is implemented by a non-volatile memory such as a hard diskor a flash memory and stores various programs and data. Morespecifically, storage 110 holds an operating system (OS) 112, ameasurement program 114, two-dimensional image data 116, and ameasurement result 118.

Operating system 112 provides an environment for processor 102 toexecute a program. Measurement program 114 implements a film thicknessmeasurement method or a refractive index measurement method according tothe present embodiment as will be described later. Two-dimensional imagedata 116 is data obtained by imaging portion 16 of measurement opticalsystem 10. Measurement result 118 includes a result obtained byexecution of measurement program 114.

Communication interface 120 mediates data transmission betweenprocessing device 100 and measurement optical system 10, obtainstwo-dimensional image data from measurement optical system 10, or givesvarious instructions to measurement optical system 10. Network interface122 mediates data transmission between processing device 100 and anexternal server, transmits a measurement result or the like to theserver, or receives a program from the server.

Medium drive 124 reads necessary data from a recording medium 126 (forexample, an optical disc) which stores a program to be executed byprocessor 102 and has the data stored in storage 110. Measurementprogram 114 to be executed by processing device 100 may be installedthrough recording medium 126 or downloaded from a server through networkinterface 122.

Measurement program 114 may call in a prescribed sequence at prescribedtiming, a necessary module from among program modules provided as a partof operating system 112 to have processing performed. In such a case,measurement program 114 without including such a module is alsoencompassed in the technical scope of the present invention. Measurementprogram 114 may be provided as being incorporated as a part of anotherprogram.

Functions provided by execution of measurement program 114 by processor102 of processing device 100 may be performed in the entirety or in partby dedicated hardware.

C. Overview of Method of Measuring Optical Characteristics

Overview of a method of measuring optical characteristics with theoptical measurement apparatus including the imaging spectroscope shownin FIG. 1 or 2 will now be described. The optical measurement apparatusaccording to the present embodiment measures optical characteristicssuch as an in-plane film thickness distribution of sample S withtwo-dimensional image 150 including wavelength information and positioninformation.

In measuring an in-plane film thickness distribution of sample S withthe imaging spectroscope, a plurality of measurement points are linearlyarranged, and hence positional relation with respect to measurementoptical system 10 is different among measurement points.

FIG. 6 is a diagram for illustrating incidence of measurementinterference light on measurement optical system 10 of the opticalmeasurement apparatus according to the present embodiment. Referring toFIG. 6, measurement interference light Lc from a central portion ofmeasurement line 24 produced on sample S propagates through an opticalpath substantially similar to the optical axis of measurement opticalsystem 10. On the other hand, measurement interference light Le from anend portion of measurement line 24 is incident on measurement opticalsystem 10 at a certain angle of incidence θ. Information which appearsin two-dimensional image 150 is different between measurement points onmeasurement line 24 due to the presence of such angle of incidence θ.

Therefore, in the method of measuring optical characteristics accordingto the present embodiment, angle of incidence θ at the time whenmeasurement interference light from sample S is incident on measurementoptical system 10 is taken into consideration. In measurement of anin-plane film thickness distribution of sample S, substantially,information in the position direction of two-dimensional image 150output from measurement optical system 10 is corrected. Morespecifically, as will be described later, processing device 100calculates a modification factor depending on an angle of incidence onmeasurement optical system 10 from each measurement point in associationwith a region in two-dimensional image 150 corresponding to eachmeasurement point in a measurement target irradiated with measurementlight. Processing device 100 then calculates optical characteristics ofsample S by applying the corresponding modification factor to each pixelvalue included in two-dimensional image 150.

Depending on sample S, a refractive index of sample S has wavelengthcharacteristics. In this case, such wavelength characteristics are takeninto consideration. In measuring an in-plane film thickness distributionof sample S, substantially, information in the wavelength direction oftwo-dimensional image 150 output from measurement optical system 10 maybe corrected.

For the sake of convenience of description, a method of measuringoptical characteristics taking into consideration both of (1) influenceby an angle of incidence of measurement interference light and (2)wavelength characteristics of a refractive index of sample S will bedescribed in detail, however, (2) wavelength characteristics of arefractive index of sample S do not have to be taken into considerationin some cases.

A film thickness measurement method of measuring a film thickness ofsample S (alternatively, an in-plane film thickness distribution) and arefractive index measurement method of measuring a refractive index ofsample S will be described below as typical examples of the method ofmeasuring optical characteristics according to the present embodiment.The method of measuring optical characteristics according to the presentembodiment is applicable not only to measurement of a film thicknessand/or a refractive index but also to measurement of any opticalcharacteristics.

D. Theoretical Explanation of Film Thickness Measurement Method

A film thickness measurement method according to the present embodimentwill now theoretically be explained.

FIGS. 7A and 7B are diagrams for illustrating principles of the filmthickness measurement method according to the present embodiment.Referring to FIG. 7A, an example in which a sample of a thin film(having a film thickness d₁) is arranged in air (a medium 0) isconsidered. An intensity transmittance T(1−R) and an intensityreflectance R in consideration of multiple reflection caused in sample S(a medium 1) are as shown in formulae (1) and (2) below, respectively.

$\begin{matrix}{T = \frac{\left( {1 - r_{01}^{2}} \right)^{2}}{1 + r_{01}^{4} - {2r_{01}^{2}\mspace{14mu}\cos\mspace{14mu} 2\beta_{1}}}} & (1) \\{R = \frac{2{r_{01}^{2}\left( {1 - {\cos\mspace{14mu} 2\beta_{1}}} \right)}}{1 + r_{01}^{4} - {2r_{01}^{2}\mspace{14mu}\cos\mspace{14mu} 2\beta_{1}}}} & (2)\end{matrix}$

n₁ represents a refractive index of sample S (medium 1), n₀ represents arefractive index of air (medium 0), and λ represents a wavelength. Inthe formulae above, an amplitude reflectance r₀₁ represents an amplitudereflectance in an optical path of medium 0→medium 1→medium 0. A phasedifference factor β₁ produced as a result of propagation of lightthrough sample S shown in FIG. 7A can be expressed as in a formula (3)below.

$\begin{matrix}{\beta_{1} = \frac{2\pi\; n_{1}d_{1}\mspace{14mu}\cos\mspace{14mu}\theta_{1}}{\lambda}} & (3)\end{matrix}$

As shown in FIG. 7B, in consideration of an example in which an angle ofincidence of light on sample S is denoted as θ₀, an angle of refractionof light produced in sample S is denoted as θ₁. Relation of n₀·sinθ₀=n₁·sin θ₁ (Snell's law) is satisfied between angle of incidence θ₀and angle of refraction θ₁. A wave number K₁ as shown in a formula (4)below is introduced by using relation between angle of incidence θ₀ andangle of refraction θ₁. Wave number K₁ corresponds to a parameter forfacilitating Fourier transform for measuring a film thickness. With wavenumber K₁, a phase angle β₁ in sample S can be defined as shown in aformula (5) below.

$\begin{matrix}{{K_{1} \equiv \frac{2\pi\; n_{1}\mspace{14mu}\cos\mspace{14mu}\theta_{1}}{\lambda}} = {\frac{2\pi\; n_{1}}{\lambda}\sqrt{1 - \left( {\frac{n_{0}}{n_{1}}\sin\mspace{14mu}\theta_{0}} \right)^{2}}}} & (4) \\{\beta_{1} = {K_{1}d_{1}}} & (5)\end{matrix}$

Wave number K₁ shown in the formula (4) above includes angle ofincidence θ₀, and a film thickness in consideration of a difference inangle of incidence θ₀ corresponding to each measurement point can becalculated by using such wave number K₁.

Considering Fourier transform with respect to phase angle β₁, cos 2β₁representing a phase factor is non-linear with respect to intensityreflectance R, and fast Fourier transform (FFT) cannot be applied as itis. Then, after conversion to a function with linearity with respect tophase factor cos 2β₁ by introducing a specific variable, Fouriertransform is performed. By way of example, a wave-number-convertedtransmittance T′ (≡1/T) or a wave-number-converted reflectance R′(≡R/(1−R)) which is a linear formula with respect to phase factor cos2β₁ is introduced. Specifically, wave-number-converted transmittance T′and wave-number-converted reflectance R′ are derived from the formulae(1) and (2) above as in formulae (6) and (7) below.

$\begin{matrix}{T^{\prime} = {{\frac{1 + r_{01}^{4}}{\left( {1 - r_{01}^{2}} \right)^{2}} - {\frac{2r_{01}^{2}}{\left( {1 - r_{01}^{2}} \right)^{2}}\cos\mspace{14mu} 2\beta_{1}}} \equiv {T_{a} + {T_{b}\mspace{14mu}\cos\mspace{14mu} 2K_{1}d_{1}}}}} & (6) \\{R^{\prime} = {{\frac{2r_{01}^{2}}{\left( {1 - r_{01}^{2}} \right)^{2}}\left( {1 - {\cos\mspace{14mu} 2\beta_{1}}} \right)} \equiv {R_{a} + {R_{b}\mspace{14mu}\cos\mspace{14mu} 2K_{1}d_{1}}}}} & (7)\end{matrix}$

Furthermore, in a power spectrum P(K₁) obtained through Fouriertransform of wave-number-converted transmittance T′ shown in the formula(6) or wave-number-converted reflectance R′ shown in the formula (7)above, a peak appears at a position corresponding to film thickness d₁of sample S. By calculating a position of a peak which appears in powerspectrum P(K₁), film thickness d₁ of sample S is determined.

Reference is to be made to Japanese Patent Laying-Open No. 2009-092454for details of wave-number-converted transmittance T′ andwave-number-converted reflectance R′.

Thus, a modification factor depending on an angle of incidence on themeasurement optical system from each measurement point includes wavenumber K₁ representing a parameter including wavelength λ of measurementlight and refractive index n₁ of sample S. Wave number K₁ may becalculated in consideration of wavelength-dependency of a refractiveindex of sample S. Then, a film thickness d is determined throughFourier transform with respect to a row of corresponding wave numbersK₁(i, j), of a row of values resulting from conversion in accordancewith a relational expression (for example, R/(1−R) or 1/T) forlinearizing a pixel value of a two-dimensional image corresponding to ameasurement point of interest with respect to a phase factor (awave-number-converted transmittance distribution T′(i, j) or awave-number-converted reflectance distribution R′(i, j)).

As set forth above, when angle of incidence θ₀ of measurementinterference light on sample S cannot be regarded as zero, a filmthickness of sample S in consideration of influence by angle ofincidence θ₀ can be calculated by introducing wave number K₁ includingangle of incidence θ₀.

A method of calculating angle of incidence θ₀ will now be described. Asdescribed above, in the film thickness measurement method according tothe present embodiment, angle of incidence θ₀ corresponding to eachmeasurement point should be calculated. Each measurement point can beset for each pixel or a set of pixels which is a set of a plurality ofadjacent pixels in two-dimensional image 150 output from measurementoptical system 10.

FIGS. 8A and 8B are diagrams showing examples of two-dimensional image150 handled in the optical measurement apparatus according to thepresent embodiment. Since the light reception surface of imaging device160 and two-dimensional image 150 are in a one-to-one correspondence, acoordinate representing any position on the light reception surface ofimaging device 160 indicates a corresponding position in two-dimensionalimage 150.

Essentially, angle of incidence θ₀ should be calculated for a positioncorresponding to each channel of imaging device 160. When the number ofchannels of imaging device 160 is sufficiently large for an angle ofview ϕ of measurement optical system 10, a set of adjacent channels maybe regarded as one pixel of two-dimensional image 150, and angle ofincidence θ₀ may be calculated for each pixel. Gathering of such aplurality of adjacent channels is referred to as “binning” below.

FIG. 9 is a diagram for illustrating binning processing in calculatingangle of incidence θ₀ used in the film thickness measurement methodaccording to the present embodiment. As shown in FIG. 9, a prescribednumber of adjacent channels arranged in the position direction among aplurality of channels constituting imaging device 160 are processedtogether. Imaging device 160 has a resolution of C_(x) channels×C_(y)channels, and can output two-dimensional image 150 corresponding to thisnumber of channels. By gathering adjacent channels, processing isaccelerated.

The number of channels gathered in the position direction is referred toas a “binning factor B_(y).” Binning factor B_(y) is preferably a commondivisor of the number of channels C_(y). By setting binning factor B_(y)to “1”, angle of incidence θ₀ in accordance with the number of channelsof imaging device 160 is calculated.

Though FIG. 9 shows an example in which a plurality of channels in theposition direction are set as one pixel, a plurality of channels also inthe wavelength direction may be set as one pixel. Namely, a binningfactor B_(x) in the wavelength direction may be introduced.

In the description below, a position of any pixel among a plurality ofpixels defined in two-dimensional image 150 is defined based oncombination of a wavelength-direction pixel number (represented below asa “variable i”) and a position-direction pixel number (represented by a“variable j” or a “variable j′” below). Position-direction pixel numberj is expressed with an integer which satisfies a condition of1≤j≤C_(y)/B_(y).

FIG. 8A shows a coordinate system when the lower left of the sheet planeis defined as the origin coordinate (1, 1). In this case, a coordinateat the upper right of the sheet plane is defined as (C_(x)/B_(x),C_(y)/B_(y)). FIG. 8B shows a coordinate system when the center in theposition direction is defined as the origin coordinate (1, 0). In thecoordinate system shown in FIG. 8B, angle of incidence θ₀ correspondingto a pixel at the center in the position direction, that is, on astraight line connecting the coordinate (1, 0) and a coordinate(C_(x)/B_(x), 0) to each other is zero. Relation of j′=j−C_(y)/2B_(y) issatisfied between position-direction pixel number j′ andposition-direction pixel number j.

The coordinate system shown in FIG. 8A is advantageous in simplificationof processing of wavelength information and position informationincluded in two-dimensional image 150, and the coordinate system shownin FIG. 8B is advantageous in simplification of processing incalculation of angle of incidence θ₀ corresponding to each measurementpoint.

Angle of incidence θ₀ at a measurement point corresponding toposition-direction pixel number j (or position-direction pixel numberj′) of two-dimensional image 150 will be reviewed below.

FIG. 10 is a diagram for illustrating a method of calculating angle ofincidence θ₀ used in the film thickness measurement method according tothe present embodiment. FIG. 10 shows an example in which a measurementline is regarded as an arc (a measurement line 24′) and an example inwhich the measurement line is regarded as a straight line (measurementline 24) in transmissive optical measurement apparatus 1 shown in FIG. 1by way of example. Angle of incidence θ₀ is calculated with any examplebeing adopted.

In FIG. 10, b represents a length of imaging device 160 in the positiondirection, f represents a focal length of object lens 12, and hrepresents a height h of object lens 12. Length b, focal length f, andheight h are expressed with the same unit (for example, mm). ϕrepresents angle of view ϕ of measurement optical system 10(=Atan(b/2f)).

When the measurement line is regarded as the arc (measurement line 24′),angle of incidence θ₀ corresponding to position-direction pixel numberj′ is derived as in a formula (8-1) below. The formula (8-1) definesangle of incidence θ₀ by using position-direction pixel number j′ whenangle of view ϕ and the center in the position direction are set tozero. A formula (8-2) can be derived by deforming the formula (8-1) witha relational expression (ϕ=Atan(b/2f)) for angle of view ϕ and arelational expression (j′=j−C_(y)/2B_(y)) for the position-directionpixel number.

$\begin{matrix}{{\theta_{0}\left( j^{\prime} \right)} = {j^{\prime} \cdot \frac{2B_{y}}{C_{y}} \cdot \phi}} & \left( {8\text{-}1} \right) \\{{\theta_{0}(j)} = {\frac{2B_{y}}{C_{y}}{\left( {j - \frac{C_{y}}{2B_{y}}} \right) \cdot {\tan^{- 1}\left( \frac{b}{2f} \right)}}}} & \left( {8\text{-}2} \right)\end{matrix}$

Alternatively, when the measurement line is regarded as the straightline (measurement line 24), angle of incidence θ₀ corresponding toposition-direction pixel number j′ is derived as in a formula (9-1)below. The formula (9-1) defines angle of incidence θ₀ by usingposition-direction pixel number j′ when angle of view ϕ and the centerin the position direction are set to zero. A formula (9-2) can bederived by deforming the formula (9-1) by using the relationalexpression (ϕ=Atan(b/2f)) for angle of view ϕ and the relationalexpression (j′=j−C_(y)/2B_(y)) for the position-direction pixel number.

$\begin{matrix}{{\theta_{0}\left( j^{\prime} \right)} = {\tan^{- 1}\left( {\frac{2\mspace{14mu}\tan\mspace{14mu}\phi}{C_{y}} \cdot j^{\prime}} \right)}} & \left( {9\text{-}1} \right) \\{{\theta_{0}(j)} = {\tan^{- 1}\left\{ {\frac{b}{C_{y}f}\left( {j - \frac{C_{y}}{2B_{y}}} \right)} \right\}}} & \left( {9\text{-}2} \right)\end{matrix}$

In the formulae (8-1), (8-2), (9-1), and (9-2) above, each channel ofimaging device 160 is handled as a point with its magnitude beingignored. Though observed transmitted light or reflected light should beexpressed with a value resulting from integration of changes in anglecorresponding to magnitude of one channel in a strict sense, magnitudeof one channel is sufficiently smaller than a length of a range ofimaging, and change in angle is ignorable. Therefore, transmitted lightor reflected light can be represented by a value for transmitted lightor reflected light from one point.

A formula (10) below can be derived by defining wave number K₁ withwavelength-direction pixel number i and position-direction pixel numberj of a two-dimensional image, with n₀=1 (a refractive index of air)being set, in the formula (4) above.

$\begin{matrix}{{K_{1}\left( {i,j} \right)} = {\frac{2\pi\;{n_{1}\left( {i,j} \right)}}{\lambda\left( {i,j} \right)}\sqrt{1 - \left( \frac{\sin\mspace{14mu}{\theta_{0}(j)}}{n_{1}\left( {i,j} \right)} \right)^{2}}}} & (10)\end{matrix}$

In the formula (10), a wavelength conversion formula λ(i, j)representing relation between a position of a pixel in two-dimensionalimage 150 and a wavelength can be determined in advance by wavelengthcalibration of measurement optical system 10. Wavelength calibrationincludes an operation to allocate a value for corresponding wavelength λto each wavelength-direction pixel number i, for each position-directionpixel number j.

A refractive index n₁(i, j) of sample S (that is, refractive indexn₁(λ)) can be obtained in advance with a measurement apparatus capableof optical constant analysis (for example, a thickness monitor based onmicroscopic spectrophotometry). In the formula (10), angle of incidenceθ₀(j) corresponding to each measurement point is defined in accordancewith the formula (8-2) or (9-2) above. By substituting this value intothe formula (10), wave number K₁(i, j) at a pixel position (i, j) can bedetermined. Wave number K₁ is thus calculated for each pixel position(i, j) in the two-dimensional image in consideration of magnitude ofcorresponding angle of incidence θ₀(j).

A film thickness in consideration of both of (1) influence by an angleof incidence of measurement interference light and (2) wavelengthcharacteristics of a refractive index of sample S can be determinedbased on relation between wave number K₁(i, j) at pixel position (i, j)and an actually measured value.

In a more specific calculation procedure, the optical measurementapparatus according to the present embodiment is used to obtain atransmittance distribution T(i, j) or a reflectance distribution R(i, j)of sample S. In succession, wave number distribution characteristics inwhich the abscissa represents wave number K₁(i, j) and the ordinaterepresents a wave-number-converted transmittance distribution T′(i, j)or a wave-number-converted reflectance distribution R′(i, j) aregenerated for each position-direction pixel number j. Power spectrumP(K₁) is calculated by subjecting the generated wave number distributioncharacteristics to Fourier transform, and a film thickness distribution(an in-plane film thickness distribution) of sample S in considerationof wavelength-dependency of an angle of incidence and a refractive indexcan be determined based on a peak which appears in calculated powerspectrum P(K₁).

As described above, wave number K₁ is calculated for each pixel position(i, j) in an imaging device including a two-dimensional light receptionsurface in accordance with the formula above, based on angle ofincidence θ₀(j) at each measurement point on the measurement line,refractive index n₁(λ) in consideration of a wavelength dispersion, andwavelength λ. Then, wave-number-converted transmittance distributionT′(i, j) or wave-number-converted reflectance distribution R′(i, j) isgenerated from transmittance distribution T(i, j) or reflectancedistribution R(i, j) of sample S obtained by actual measurement, byusing a relational expression for linearization with respect to phasefactor cos 2β (for example, R/(1−R) or 1/T). By applying wave numberK₁(i, j) to such generated wave-number-converted transmittancedistribution T′ or wave-number-converted reflectance distribution T′, apower spectrum P(m, j) subjected to Fourier transform (a parameter mrepresenting a discrete value corresponding to the abscissa of the powerspectrum) can be obtained. A value for a film thickness at eachmeasurement point of sample S is calculated based on a peak whichappears in power spectrum P(m, j).

Typically, any of a method of using discrete Fourier transform such asfast Fourier transform (FFT) and an optimization method such as amaximum entropy method (which is also referred to as “MEM” below) can beadopted as a method of specifying a wave number component large inamplitude (a peak) from wave number distribution characteristics. Whendiscrete Fourier transform is employed, a power of two such as 512,1024, 2048, 4096, . . . is used as a discrete value in a frequencydomain.

E. Specific Example of Film Thickness Measurement Method

A method of measuring a film thickness based on the theoreticalexplanation of the film thickness measurement method described abovewill now be described. In the description below, a method of determininga film thickness of sample S based on a peak which appears in powerspectrum P(K₁) obtained by subjecting wave-number-convertedtransmittance T′ or wave-number-converted reflectance R′ to Fouriertransform (what is called the FFT method) and a method of determining afilm thickness of sample S by shape comparison (fitting) betweenobtained wavelength distribution characteristics (an actually measuredvalue of a transmittance spectrum or a reflectance spectrum) andwavelength distribution characteristics calculated with a model formula(a theoretical formula) including an angle of incidence, a refractiveindex, a wavelength, and a film thickness as parameters (what is calledan optimization method) will be described.

Though any one of these film thickness measurement methods may beincorporated, the film thickness measurement method is preferablyselectable as appropriate depending on a film thickness or a materialfor sample S.

(e1: Processing Procedure (No. 1) in Film Thickness Measurement Method)

A processing procedure (No. 1) in the film thickness measurement methodaccording to the present embodiment will initially be described. Theprocessing procedure (No. 1) in the film thickness measurement method isa method of determining a film thickness of sample S based on a peakwhich appears in power spectrum P(K₁) with respect to wave number K₁.

FIG. 11 is a flowchart showing the processing procedure (No. 1) in thefilm thickness measurement method according to the present embodiment.FIG. 12 is a diagram for illustrating processing contents in theprocessing procedure (No. 1) in the film thickness measurement methodshown in FIG. 11.

Referring to FIG. 11, initially, processing device 100 calculates angleof incidence θ₀ corresponding to each measurement point, of measurementinterference light incident on measurement optical system 10 (stepS100).

Specifically, processing device 100 calculates angle of incidence θ₀corresponding to each measurement point set on the measurement line(corresponding to each pixel in the position direction oftwo-dimensional image 150 determined depending on the number of channelsand the binning factor of imaging device 160) for eachposition-direction pixel number j. Namely, processing device 100calculates θ₀(j) in the formula (10) above for all position-directionpixel numbers j. θ₀(j) may be a radian value or a value of atrigonometric function (for example, sin θ₀(j) or cos θ₀(j)). Any valueadapted to subsequent operation processing may be adopted so long as thevalue represents magnitude of an angle of incidence.

A value of angle of incidence θ₀ corresponding to each measurement pointobtained as a result of step S100 does not have to be calculated again,so long as the setting or the configuration of the optical measurementapparatus is the same. Therefore, when angle of incidence θ₀corresponding to each measurement point has been calculated in advance,processing in step S100 may be skipped.

Processing device 100 obtains refractive index n₁(λ) in consideration ofwavelength dispersion of sample S based on a result of measurement forsample S with a measurement apparatus capable of optical constantanalysis (for example, a thickness monitor based on microscopicspectrophotometry) (step S102).

Refractive index n₁(λ) of sample S obtained in step S102 does not haveto be obtained again so long as a material for sample S is the same.Therefore, so long as identity of sample S corresponding to refractiveindex n₁(λ) obtained earlier is maintained, processing in step S102 maybe skipped. When a refractive index can be regarded as constantregardless of a wavelength, a constant value may be set for refractiveindex n₁(λ).

Processing device 100 calculates a wavelength conversion formula λ(i, j)representing relation between a pixel position in two-dimensional image150 and wavelength λ based on a result of wavelength calibration formeasurement optical system 10 (step S104). In step S104, wavelength λ isbrought in correspondence with pixel position (i, j) in two-dimensionalimage 150. Wavelength λ can be expressed in matrix with pixel position(i, j) in two-dimensional image 150 being defined as a parameter (thatis, wavelength λ=λ(i, j)).

Basically, wavelength conversion formula λ(i, j) calculated in step S104does not have to be calculated again so long as the setting or theconfiguration of measurement optical system 10 is the same. Therefore,so long as wavelength conversion formula λ(i, j) calculated earlier caneffectively be made use of, processing in step S104 may be skipped.

The order of performing processing in steps S100, S102, and S104 is notparticularly limited. Timing to perform processing in steps S100, S102,and S104 may be different.

In succession, processing device 100 expands wave number K₁ shown in theformula (4) above for pixel position (i, j) in two-dimensional image150. Processing device 100 calculates wave number K₁(i, j) for eachpixel position (i, j) in two-dimensional image 150 (step S106).

As shown in the formula (4) above, in the film thickness measurementmethod according to the present embodiment, wave number K₁ which takeswavelength λ, refractive index n₁, and angle of incidence θ₀ asvariables is introduced.

Among the variables included in wave number K₁, refractive index n₁ is afunction of wavelength λ. Since wavelength λ can be defined bywavelength conversion formula λ(i, j), refractive index n₁ can bedefined with pixel position (i, j) in two-dimensional image 150 beingdefined as a parameter (that is, refractive index n₁=n₁(λ)=n₁(i, j) andwavelength λ=λ(i, j)). Angle of incidence θ₀ corresponding to eachmeasurement point which is calculated in step S100 can be used as angleof incidence θ₀. Angle of incidence θ₀ is defined only byposition-direction pixel number j (that is, angle of incidenceθ₀=θ₀(j)).

As set forth above, since all of wavelength λ, refractive index n₁, andangle of incidence θ₀ can be defined with measurement point (i, j)corresponding to each pixel in two-dimensional image 150, a value ofeach of them is uniquely determined by designating pixel position (i,j). Processing device 100 generates wave number K₁(i, j) representing avalue of wave number K₁ for each pixel position (i, j) by applyingvalues for wavelength λ, refractive index n₁, and angle of incidence θ₀determined for each pixel position (i, j). As shown in FIG. 12,generated wave number K₁(i, j) corresponds to each pixel intwo-dimensional image 150.

Processing in steps S100 to S106 above corresponds to a preparationstep.

Sample S is set in optical measurement apparatus 1, and processingdevice 100 obtains two-dimensional image 150 imaged while sample S isirradiated with measurement interference light (step S110). Processingdevice 100 obtains an actually measured value of transmittancedistribution T(i, j) (or reflectance distribution R(i, j)) for aplurality of measurement points on measurement line 24 of sample S. Asshown in FIG. 12, two-dimensional image 150 having the wavelengthdirection and the position direction is obtained. The wavelengthdirection corresponds to wavelength λ for specific position-directionpixel number j.

In succession, processing device 100 sets position-direction pixelnumber j=1 (step S112). Setting of position-direction pixel number jmeans setting a pixel row corresponding to specific position-directionpixel number j in two-dimensional image 150 as a target as shown in FIG.12.

Processing device 100 generates wave number distribution characteristicsin which the abscissa represents wave number K₁(i, j) and the ordinaterepresents wave-number-converted transmittance distribution T′(i, j) (orwave-number-converted reflectance distribution R′(i, j)) from obtainedtransmittance distribution T(i, j) (or reflectance distribution R(i, j))by referring to wave number K₁(i, j) calculated in step S106 (stepS114).

More specifically, as shown in FIG. 12, processing device 100 extractsvalues in a row corresponding to current position-direction pixel numberj from wave number K₁(i, j) and applies the values to values of a pixelrow extracted from two-dimensional image 150.

Processing device 100 thus converts obtained wavelength distributioncharacteristics (correspondence between each wavelength and a value of atransmittance or a reflectance at that wavelength) into correspondencewith a converted value of the transmittance or the reflectancecalculated in accordance with wave number distribution characteristics.The wave number distribution characteristics include correspondencebetween a wave number determined by a function including an angle ofincidence, a refractive index, and a wavelength as parameters and avalue of a transmittance or a reflectance at that wave number.Alternatively, the wave number distribution characteristics includecorrespondence between a wave number and a converted value of thetransmittance or the reflectance calculated in accordance with arelational expression for linearization with respect to phase factor cos2β (for example, R/(1−R) or 1/T).

In succession, processing device 100 generates power spectrum P(K₁) bysubjecting the wave number distribution characteristics generated instep S114 in which the abscissa represents wave number K₁(i, j) toFourier transform with respect to wave number K₁(i, j) (step S116).Processing device 100 subjects a row of values resulting from conversionin accordance with a relational expression for linearization of pixelvalues of two-dimensional image 150 corresponding to a measurement pointof interest with respect to a phase factor to Fourier transform withrespect to a row of corresponding wave numbers.

Processing device 100 calculates film thickness d₁(j) at a measurementpoint corresponding to current position-direction pixel number j bycalculating a peak position which appears in power spectrum P(K₁)generated in step S116 (step S118). Processing device 100 determines afilm thickness at a measurement point of interest based on a peakposition which appears in power spectrum P(K₁) obtained through Fouriertransform. A wave number component (that is, film thickness d₁(j)) largein amplitude may be determined by using the optimization method insteadof Fourier transform.

Processing device 100 determines whether or not currentposition-direction pixel number j is a final value (step S120). Whencurrent position-direction pixel number j is not the final value (NO instep S120), processing device 100 increments current position-directionpixel number j by one (step S122) and repeats processing in step S114 orlater.

When current position-direction pixel number j is the final value (YESin step S120), processing device 100 generates a film thicknessdistribution on measurement line 24 of sample S by aggregating filmthicknesses d₁(j) calculated at position-direction pixel numbers j from1 to the final value (step S124). Processing device 100 aggregates thefilm thicknesses determined for a plurality of measurement points andoutputs the resultant aggregate as the film thickness distribution.

Processing device 100 determines whether or not a condition to quitmeasurement of a film thickness of sample S has been satisfied (stepS126). When the condition to quit measurement of a film thickness ofsample S has not been satisfied (NO in step S126), processing device 100repeats the processing in step S110 or later.

In contrast, when the condition to quit measurement of a film thicknessof sample S has been satisfied (YES in step S126), processing device 100integrates film thickness distributions successively calculated in stepS124 and outputs the resultant film thickness distribution as a filmthickness distribution (an in-plane film thickness distribution) at themeasurement surface of sample S (step S128). Then, the process ends.

In the processing procedure (No. 1) in the film thickness measurementmethod described above, description has been given with attention beingpaid to wave number K₁ as a modification factor depending on angle ofincidence θ₀ on measurement optical system 10 from a measurement point,however, the modification factor is not limited thereto. For example,the modification factor is a concept which may coverwave-number-converted transmittance T′ (≡1/T) or wave-number-convertedreflectance R′ (≡R/(1−R)) described above.

(e2: Measurement Example)

A measurement example obtained with the film thickness measurementmethod (No. 1) according to the present embodiment will now be shown.

FIG. 14 is a diagram showing one example of a film thickness trendobtained with the film thickness measurement method according to thepresent embodiment. A 1-mm square polyethylene thin film (an outerdimension of 1 mm×1 mm) was employed as sample S.

A film thickness in each of two patterns of with modification (thepresent embodiment) and without modification of angle of incidence θ₀was measured, with a measurement point in sample S (that is, angle ofincidence θ₀) being sequentially varied. A lens having a focal lengthf=16 mm was employed as object lens 12.

A wavelength distribution of a refractive index of the polyethylene thinfilm actually measured with a thickness monitor based on microscopicspectrophotometry was adopted as refractive index n₁. FIG. 13 is adiagram showing one example of a wavelength distribution of refractiveindex n₁(λ) of the polyethylene thin film. By way of example, a Cauchydispersion formula as shown in a formula (11) below is used forrefractive index n₁(λ) shown in FIG. 13.

$\begin{matrix}{{n_{1}(\lambda)} = {C_{0} + \frac{C_{1}}{\lambda^{2}} + \frac{C_{2}}{\lambda^{4}}}} & (11)\end{matrix}$

In the example shown in FIG. 13, coefficients are set as C₀=1.533731,C₁=429.0333, and C₂=2.09247×10⁸.

FIG. 14 shows variation in measured film thickness with variation inangle of incidence θ₀. As shown in FIG. 14, it can be seen that the filmthickness trend becomes flatter by taking into consideration angle ofincidence θ₀. It is shown that a film thickness distribution (anin-plane film thickness distribution) of sample S can more accurately bemeasured.

(e3: Simulation Example)

For example, a theoretical value of transmittance spectrum T(λ) at eachmeasurement point can be calculated based on the formulae (1), (5),(8-2), and (10) above. FIG. 15 is a diagram showing one example of atwo-dimensional image (1200 pixels×1920 pixels) exhibiting atransmittance spectrum in accordance with a theoretical formulaaccording to the present embodiment. The two-dimensional imageexhibiting the transmittance spectrum shown in FIG. 15 is obtained whenfilm thickness d₁ is (uniformly) set to 10 [μm] and an amplitudereflectance |r₀₁| is set to 0.2.

A wavelength distribution of a refractive index of the polyethylene thinfilm actually measured with a thickness monitor based on microscopicspectrophotometry as shown in FIG. 13 described above was adopted asrefractive index n₁. By way of example, the Cauchy dispersion formula asshown in the formula (11) above is used for refractive index n₁(λ) shownin FIG. 13.

In the example shown in FIG. 13, coefficients are set as C₀=1.533731,C₁=429.0333, and C₂=2.09247×10⁸.

FIG. 16 is a graph showing transmittance spectrum T(λ) corresponding toposition-direction pixel number j in the two-dimensional image(theoretical value) shown in FIG. 15. FIG. 16 shows transmittancespectrum T(λ) on a line of each position-direction pixel number j=1,100, 200, . . . , 1200. The reason why transmittance spectrum T(λ) isnot consistent in FIG. 16 is because of a difference in angle ofincidence θ₀ corresponding to each measurement point.

FIGS. 17A and 17B are graphs showing wave-number-convertedtransmittances T′(K₁) calculated from transmittance spectrum T(λ) shownin FIG. 16. FIG. 17A shows wave-number-converted transmittance T′(K₁)calculated with wave number K₁ with angle of incidence θ₀ being assumedas zero for all position-direction pixel numbers j. FIG. 17B showswave-number-converted transmittance T′(K₁) calculated with wave numberK₁ in consideration of angle of incidence θ₀ in accordance with allposition-direction pixel numbers j.

In transmittance spectrum T(λ) shown in FIG. 16, a period of aninterference waveform is different owing to a difference inposition-direction pixel number j (that is, angle of incidence θ₀).Therefore, it can be seen that wave-number-converted transmittanceT′(K₁) is also inconsistent as shown in FIG. 17A when wave number K₁ notin consideration of a difference in angle of incidence θ₀ is used.

On the other hand, it can be seen that, by using wave number K₁ inconsideration of angle of incidence θ₀ in accordance withposition-direction pixel number j, wave-number-converted transmittanceT′(K₁) is consistent for all position-direction pixel numbers j. Sincewave-number-converted transmittance T′(K₁) is substantially the sameregardless of position-direction pixel number j, a correct filmthickness can be calculated from any wave-number-converted transmittanceT′(K₁).

FIG. 18 is a diagram showing one example of a film thickness trendcalculated from wave-number-converted transmittances T′(K₁) shown inFIGS. 17A and 17B. Referring to FIG. 18, without modification of anangle of incidence shown in FIG. 17A, a film thickness is maximized atposition-direction pixel number j=600 at which angle of incidence θ₀ iszero, and a film thickness decreases toward opposing ends because ofincrease in angle of incidence θ₀.

In contrast, it can be seen that, with modification of an angle ofincidence shown in FIG. 17B, 10 [μm] which is a proper film thickness iscorrectly calculated at all position-direction pixel numbers j.

As set forth above, by adopting the theoretical formula according to thepresent embodiment, physical characteristics in consideration of angleof incidence θ₀ corresponding to a measurement point can accurately bereproduced. Accurate fitting can be achieved by using the formulae asabove.

(e4: Processing Procedure (No. 2) in Film Thickness Measurement Method)

In the processing procedure (No. 1) in the film thickness measurementmethod described above, a method of calculating a film thickness bysubjecting wave number distribution characteristics calculated fromtwo-dimensional image 150 subjected to measurement by introducing wavenumber K₁ to Fourier transform is exemplified. A method of calculating afilm thickness by fitting between a theoretically generatedtwo-dimensional image and two-dimensional image 150 subjected tomeasurement instead of such a method will be described.

FIG. 19 is a schematic diagram for illustrating processing contents in aprocessing procedure (No. 2) in the film thickness measurement methodaccording to the present embodiment. Each element shown in FIG. 19 istypically implemented by execution of measurement program 114 byprocessor 102 of processing device 100.

Referring to FIG. 19, processing device 100 includes buffers 152 and156, a modeling module 154, and a fitting module 158. In theconfiguration shown in FIG. 19, modeling module 154 calculates atheoretical value of transmittance spectrum T(λ) (or reflectancespectrum R(λ)) and adjusts film thickness d₁ defining a theoreticalvalue such that correlation with an actually measured value of obtainedtransmittance spectrum T(λ) (or reflectance spectrum R(λ)) is higher.Finally, a film thickness which leads to transmittance spectrum T(λ) (orreflectance spectrum R(λ)) highest in correlation with the actuallymeasured value of transmittance spectrum T(λ) (or reflectance spectrumR(λ)) is output as a measurement result.

For the sake of convenience of description, a suffix “_(meas)” isattached to an actually measured value of a transmittance spectrum or areflectance spectrum and a suffix “_(theo)” is attached to a theoreticalvalue of a transmittance spectrum or a reflectance spectrum.

More specifically, buffer 152 stores two-dimensional image 150 (actuallymeasured value) imaged by measurement optical system 10. Buffer 156stores a two-dimensional image (theoretical value) generated by modelingmodule 154. Fitting module 158 calculates a similarity by shapecomparison (fitting) between two-dimensional image 150 (actuallymeasured value) stored in buffer 152 and the two-dimensional image(theoretical value) stored in buffer 156, and outputs a parameterupdating command to modeling module 154 so as to maximize the calculatedsimilarity. An example in which a correlation value or a correlationmatrix is used as a similarity is exemplified.

When the calculated similarity is equal to or greater than apredetermined threshold value, fitting module 158 outputs film thicknessd₁(j) at that time as a measurement result.

An initial value of film thickness d₁(j), an optical constant inconsideration of a wavelength dispersion of sample S (refractive indexn₁(λ) and an extinction coefficient k₁(λ)), wavelength conversionformula λ(i, j) determined by wavelength calibration of measurementoptical system 10, and angle of incidence θ₀(j) at each measurementpoint on measurement line 24 are input to modeling module 154. Modelingmodule 154 calculates a transmittance distribution T_(theo)(i, j, d₁(j))or a reflectance distribution R_(theo)(i, j, d₁(j)) for pixel position(i, j) and film thickness d₁(j) based on the input information. Modelingmodule 154 updates as appropriate film thickness d₁(j) in accordancewith a parameter updating command from fitting module 158. Reference isto be made to a formula (20) which will be described later for detailsof transmittance distribution T_(theo) or reflectance distributionR_(theo).

A wavelength distribution of a refractive index of the polyethylene thinfilm actually measured with a thickness monitor based on microscopicspectrophotometry as shown in FIG. 13 described above was adopted forrefractive index n₁. By way of example, the Cauchy dispersion formula asshown in the formula (11) above is used for refractive index n₁(λ) shownin FIG. 13.

In the example shown in FIG. 13, coefficients are set as C₀=1.533731,C₁=429.0333, and C₂=2.09247×10⁸.

FIG. 20 is a flowchart showing the processing procedure (No. 2) in thefilm thickness measurement method according to the present embodiment.Referring to FIG. 20, initially, processing device 100 calculates angleof incidence θ₀ corresponding to each measurement point, of measurementinterference light incident on measurement optical system 10 (stepS100). A value representing magnitude of an angle of incidencecorresponding to each measurement point is employed as a modificationfactor depending on an angle of incidence on the measurement opticalsystem from each measurement point.

Then, processing device 100 obtains refractive index n₁(λ) inconsideration of a wavelength dispersion of sample S from a result ofmeasurement for sample S with a measurement apparatus capable of opticalconstant analysis (for example, a thickness monitor based on microscopicspectrophotometry) (step S102). In succession, processing device 100calculates wavelength conversion formula λ(i, j) representing relationbetween a pixel position in two-dimensional image 150 and wavelength λbased on a result of wavelength calibration for measurement opticalsystem 10 (step S104).

Since the processing in steps S100 to S104 is the same as in steps S100to S104 in the flowchart of the processing procedure (No. 1) in the filmthickness measurement method shown in FIG. 11, detailed description willnot be repeated. The processing in steps S100 to S104 above correspondsto a preparation step.

Sample S is set in optical measurement apparatus 1, and processingdevice 100 obtains two-dimensional image 150 imaged while sample S isirradiated with measurement light (step S130). Processing device 100obtains transmittance distribution T_(meas)(i, j) (or reflectancedistribution R_(meas)(i, j)).

Processing device 100 calculates transmittance distribution T_(theo)(i,j, d₁(j)) (or reflectance distribution R_(theo)(i, j, d₁(j))) based oninformation calculated in steps S100 to S104 and the initial value offilm thickness d₁(j) (step S132). Processing device 100 adopts filmthickness d₁(j) at each measurement point as a fluctuating parameter andcalculates a theoretical value of each pixel corresponding totwo-dimensional image 150 based on refractive index n₁ of sample S, avalue in accordance with magnitude of an angle of incidencecorresponding to each measurement point, and correspondence between eachmeasurement point and pixel position (i, j) in the two-dimensionalimage.

In succession, processing device 100 calculates a similarity betweentransmittance distribution T_(meas)(i, j) (or reflectance distributionR_(meas)(i, j)) obtained in step S130 and transmittance distributionT_(theo)(i, j, d₁(j)) (or reflectance distribution R_(theo)(i, j,d₁(j))) calculated in step S132 by shape comparison therebetween (stepS134).

More specifically, processing device 100 calculates a correlation matrixor a correlation coefficient between transmittance distributionT_(meas)(i, j) (or reflectance distribution R_(meas)(i, j)) andtransmittance distribution T_(theo)(i, j, d₁(j)) (or reflectancedistribution R_(theo)(i, j, d₁(j))). A similarity for eachposition-direction pixel number j can be calculated by using thecorrelation matrix. When variation in film thickness d₁(j) in theposition direction is estimated to sufficiently be small, the filmthickness may be regarded as d₁(j)=d₁ and a one-dimensional value (thatis, a correlation value) which is summarization of the entire spectramay be calculated.

Processing device 100 determines whether or not the similaritycalculated in step S134 is equal to or greater than a predeterminedthreshold value (step S136). When the calculated similarity is smallerthan the predetermined threshold value (NO in step S136), processingdevice 100 updates film thickness d₁(j) (step S138) and repeatsprocessing in step S132 or later. Film thickness d₁(j) may be updatedfor each position-direction pixel number j in accordance with magnitudeof a corresponding similarity, or a prescribed amount may be added orsubtracted in common.

When the calculated similarity is equal to or greater than thepredetermined threshold value (YES in step S136), processing device 100aggregates current film thicknesses d₁(j) and outputs the resultantaggregate as a film thickness distribution on measurement line 24 ofsample S (step S140).

Thus, processing device 100 determines a film thickness at eachmeasurement point by adjusting a fluctuating parameter such that asimilarity between a calculated theoretical value of each pixel and eachpixel value of two-dimensional image 150 is higher. The fluctuatingparameter is adjusted such that correlation close to similitude relationis found between the calculated theoretical waveform and an actuallymeasured waveform.

In succession, processing device 100 determines whether or not acondition to quit measurement of a film thickness for sample S has beensatisfied (step S142). When the condition to quit measurement of a filmthickness for sample S has not been satisfied (NO in step S142),processing device 100 repeats the processing in step S130 or later.

In contrast, when the condition to quit measurement of a film thicknessfor sample S has been satisfied (YES in step S142), processing device100 integrates the film thickness distributions successively calculatedin step S140 and outputs the resultant film thickness distribution as afilm thickness distribution (an in-plane film thickness distribution) atthe measurement surface of sample S (step S144). Then, the process ends.

As set forth above, in the processing procedure (No. 2) in the filmthickness measurement method, a film thickness (or a film thicknessdistribution) of sample S is determined by shape comparison (fitting)between an actually measured value of a transmittance spectrum or areflectance spectrum representing wavelength distributioncharacteristics obtained from sample S and a theoretical value of atransmittance spectrum or a reflectance spectrum determined inaccordance with a model formula (theoretical formula) having angle ofincidence θ₀, refractive index n₁(λ), wavelength λ, and film thicknessd₁(j) as parameters.

More specifically, a correlation matrix (or a correlation value) withtransmittance distribution T_(meas)(i, j) (or reflectance distributionR_(meas)(i, j)) is calculated with film thickness d₁(j) being varied intransmittance distribution T_(theo)(i, j, d₁(j)) (or reflectancedistribution R_(theo)(i, j, d₁(j))), and film thickness d₁(j) highest incorrelation (that is, having a correlation coefficient closest to one)is output as a final result.

A film thickness distribution (an in-plane film thickness distribution)of sample S can be measured through the process as above.

In the processing procedure (No. 2) in the film thickness measurementmethod described above, though description has been given with attentionbeing paid to transmittance distribution T_(theo)(i, j, d₁(j)) orreflectance distribution R_(theo)(i, j, d₁(j)) calculated inconsideration of angle of incidence θ₀ as a modification factordepending on angle of incidence θ₀ on measurement optical system 10 froma measurement point, the modification factor is not limited thereto. Forexample, the modification factor is a concept which may encompass wavenumber K₁ described above.

In steps S136 and S138 described above, a range and a pitch of filmthickness parameter d₁(j) to be varied are set for transmittancedistribution T_(theo)(i, j, d₁(j)) (or reflectance distributionR_(theo)(i, j, d₁(j))), and transmittance distribution T_(theo)(i, j,d₁(j)) (or reflectance distribution R_(theo)(i, j, d₁(j))) for filmthickness value d₁(j) within the set range of variation is calculated inadvance. Then, a correlation matrix or a correlation coefficient betweentransmittance distribution T_(theo)(i, j, d₁(j)) (or reflectancedistribution R_(theo)(i, j, d₁(j))) calculated in advance and actuallymeasured transmittance distribution T_(theo)(i, j) (or reflectancedistribution R_(theo)(i, j)) may be calculated in a round-robin fashion,and film thickness value d₁(j) at which a similarity (a correlationcoefficient) is highest in a result of calculation may be determined asa film thickness at each measurement point.

(e5: Multi-Layered Film Sample)

Though processing for measuring a thickness of one layer has mainly beendescribed for the sake of convenience of description, limitation theretois not intended and a thickness of each layer in a multi-layered filmsample can be measured. A refractive index of each layer in themulti-layered film sample can also be measured.

In measuring a thickness of each layer of the multi-layered film samplein the processing procedure (No. 1) in the film thickness measurementmethod described above, a plurality of peaks in accordance withthicknesses of layers appear in power spectrum P(K₁) obtained throughFourier transform of wave-number-converted transmittance T′ orwave-number-converted reflectance R′. A thickness of each layer forminga sample of interest can be calculated by analyzing the plurality ofpeaks which appear in power spectrum P(K₁).

In measuring a thickness of each layer of the multi-layered film samplein the processing procedure (No. 2) in the film thickness measurementmethod, a thickness of each layer forming a sample of interest can becalculated by performing fitting for each layer by using a model formulaincluding an optical constant (a refractive index and an extinctioncoefficient) of each layer in consideration of a wavelength dispersionand a thickness of each layer.

(e6: In-Line Measurement/Off-Line Measurement)

Though a processing example in which a film thickness is measured insuccession to imaging of a two-dimensional image of sample S is mainlyshown in the description above, limitation to such in-line measurementor real-time measurement is not intended, and for example,two-dimensional images of sample S may successively be imaged and a filmthickness trend (an in-plane film thickness distribution) maysubsequently be output.

F. Refractive Index Measurement Method

Though refractive index n₁(λ) of sample S is measured in advance with athickness monitor based on microscopic spectrophotometry in the filmthickness measurement method described above, refractive index n₁(λ) ofsample S can also be measured with the optical measurement apparatusaccording to the present embodiment.

(f1: Overview)

Initially, a small piece of identical sample S (for example, of a 1-mmsquare) is arranged at each measurement point on the measurement lineand actually measured values (transmittance distribution T_(meas)(i, j)or reflectance distribution R_(meas)(i, j)) at the measurement pointsare successively obtained. Namely, a transmittance spectrum or areflectance spectrum in the wavelength direction (that is, adistribution of actually measured values) when position-direction pixelnumber j (that is, angle of incidence θ₀) is different for the samesample S is determined.

Unknown refractive index n₁(λ) is determined by applying such advanceinformation as film thickness d₁ being the same to transmittancedistribution T_(meas)(i, j) (or reflectance distribution R_(meas)(i, j))measured for the same sample S.

FIGS. 21 and 22 are schematic diagrams for illustrating overview of therefractive index measurement method according to the present embodiment.FIG. 21 shows an example in which refractive index n₁(λ) of sample S ismeasured by using an intensity distribution at specificposition-direction pixel number j. FIG. 22 shows an example in whichrefractive index n₁(λ) of sample S is measured by using an intensitydistribution at specific wavelength-direction pixel number i.

Referring to FIG. 21, with attention being paid to position-directionpixel number j, refractive index n₁(λ) of sample S is set to aprovisional value and then film thickness d₁(j) (j=j₁, j₂, j₃, . . . )is calculated from transmittance distribution T_(meas)(i, j) (orreflectance distribution R_(meas)(i, j)) at specific position-directionpixel number j. Since film thickness d₁ is the same, refractive indexn₁(λ) of sample S is determined such that calculated film thicknessesd₁(j) are consistent.

Referring to FIG. 22, with attention being paid to specificwavelength-direction pixel number i, unknown refractive index n₁(λ) isdetermined by applying such advance information as film thickness d₁being the same to a difference between a theoretical value and anactually measured value.

More specifically, initially, transmittance distribution T_(theo)(i, j,d₁, n₁(i)) (or reflectance distribution R_(theo)(i, j, d₁, n₁(i)) iscompared with transmittance distribution T_(meas)(i, j) (or reflectancedistribution R_(meas)(i, j)) at corresponding position-direction pixelnumber j.

Transmittance distribution T_(theo) (or reflectance distributionR_(theo)) takes a value dependent on pixel position (i, j), filmthickness d₁, and refractive index n₁(λ). Pixel position (i, j) hasalready been known and film thickness d₁ is the same regardless ofwavelength-direction pixel number i. Therefore, refractive index n₁(λ)can be determined by applying such advance information as film thicknessd₁ being the same to a result of comparison between the theoreticalvalue and the actually measured value for a plurality ofwavelength-direction pixel numbers i (i=i₁, i₂, i₃, . . . ).

Referring to FIG. 22, with attention being paid to specificwavelength-direction pixel number i as in an example in which attentionis paid to position-direction pixel number j, refractive index n₁(λ) ofsample S is set to a provisional value and then film thickness d₁(i)(i=i₁, i₂, i₃, . . . ) is calculated from transmittance distributionT_(meas)(i, j) (or reflectance distribution R_(meas)(i, j)) at specificwavelength-direction pixel number i. Since film thickness d₁ is thesame, refractive index n₁(λ) of sample S is determined such thatcalculated film thicknesses d₁(j) are consistent.

According to the refractive index measurement method according to thepresent embodiment, refractive index n₁ of sample S can be measured withthe optical measurement apparatus according to the present embodimentwithout using a dedicated measurement apparatus such as a thicknessmonitor based on microscopic spectrophotometry.

For example, a film thickness trend is obtained by setting anyrefractive index n₁ to any initial value (for example, 1 for allwavelengths) in accordance with operational processing with a functionto correct angle of incidence θ₀ as described above and varying aposition to arrange a small piece of sample S. When a set value ofrefractive index n₁ is different from an actual refractive index ofsample S, the film thickness trend does not become flat. By varying asappropriate refractive index n₁ with a least squares method, such arefractive index n₁ as achieving the flattest film thickness trend, thatis, minimizing a film thickness dispersion, can be determined.

Refractive index n₁ may be found as a constant on average for allwavelengths, or when more strict calculation of the refractive index isdesired, for example, the Cauchy dispersion formulan₁(λ)=E+(F/λ²)+(G/λ⁴) is assumed in consideration of a wavelengthdispersion, and a coefficient in each term may be found with the leastsquares method.

Alternatively, a refractive index may be calculated with such a methodas minimizing a squared residual value of a film thickness withattention being paid to a specific line relatively large in angle ofincidence.

In the refractive index measurement method described above, filmthicknesses d₁(i) at a plurality of positions in a distribution ofactually measured values are calculated based on set refractive indexn₁(λ), a modification factor corresponding to each position, and a groupof pixel values in the wavelength direction at each position. A filmthickness dispersion which is a dispersion for each calculated filmthickness d₁(i) is calculated. Then, processing for calculating filmthickness d₁(i) and processing for calculating a film thicknessdispersion are repeated with a refractive index of sample S being set toa plurality of different values. Finally, a refractive index of sample Sis determined based on the calculated film thickness dispersion.

In the present embodiment, a distribution of actually measured valuescorresponding to two-dimensional image 150 (transmittance distributionT_(meas)(i, j) or reflectance distribution R_(meas)(i, j)) is obtainedby successively arranging sample S to measurement points irradiated withmeasurement light and successively obtaining actually measured values atthe measurement points. A modification factor depending on an angle ofincidence on measurement optical system 10 from each measurement point(a value representing magnitude of an angle of incidence correspondingto each measurement point) is calculated in association with a region intwo-dimensional image 150 corresponding to each measurement point insample S irradiated with measurement light. Optical characteristicsincluding a refractive index of sample S are calculated based on a groupof pixel values in one row or a plurality of rows along any onedirection in the distribution of the actually measured values and acorresponding modification factor. In the distribution of the actuallymeasured values, such advance information as film thickness d₁ being thesame is made use of.

Each case will be described below in further detail.

(f2: Refractive Index Measurement Method (No. 1) Based on Information inWavelength Direction)

Initially, the refractive index measurement method (No. 1) based oninformation in the wavelength direction will be described. Initially, anexample in which a condition of n₁(λ)=n₁ (constant value) is satisfiedwithout taking wavelength-dependency of a refractive index of sample Sinto consideration will be described first.

In the refractive index measurement method (No. 1) based on theinformation in the wavelength direction, refractive index n₁ of sample Sis set to some initial value and film thicknesses d₁ are calculated fora transmittance spectrum (or a reflectance spectrum) at a plurality ofwavelength-direction pixel numbers i based on refractive index n₁. Then,a film thickness trend of a plurality of calculated film thicknesses d₁is evaluated. Refractive index n₁ is fitted so as to flatten the filmthickness trend. When actual refractive index n₁ of sample S isdifferent from set refractive index n₁, the film thickness trend cannotmaintain flatness. This is based on the premise that a film thickness ata fixed point in sample S should take a constant value in measurement atany angle of incidence θ₀ by adopting a calculation method inconsideration of influence by angle of incidence θ₀ of measurementinterference light as described above.

Flatness of the film thickness trend is adopted as a cost function basedon such a premise, and refractive index n₁ which minimizes a value ofthe cost function is determined. A film thickness in measurement at thefixed point in sample S at position-direction pixel number j is denotedas d₁(j). A film thickness trend curve d₁(j) with position-directionpixel number j being varied is approximated to a constant functionf(j)=μ (μ being a constant value). A sum of squared residuals S can bedefined as in a formula (12) below. Constant value μ in the formula (12)is determined with the least squares method. More specifically, aformula (13) below is obtained by finding constant value μ under such acondition that sum of squared residuals S is minimized, that is, acondition of ∂S/∂μ=0 is satisfied.

$\begin{matrix}{S = {\sum\limits_{j = 1}^{C_{y}\text{/}B_{y}}\;\left\{ {{d_{1}(j)} - \mu} \right\}^{2}}} & (12) \\{\mu = {{\frac{B_{y}}{C_{y}}{\sum\limits_{j = 1}^{C_{y}\text{/}B_{y}}\;{d_{1}(j)}}} \equiv \overset{\_}{d_{1}}}} & (13)\end{matrix}$

Constant value μ calculated in accordance with the formula (12)corresponds to an average value of film thicknesses d₁(j). Since sum ofsquared residuals S is a sum of squared residuals of the average valueof film thicknesses d₁(j), it corresponds to a dispersion of filmthicknesses d₁(j) (which is referred to as a “film thickness dispersion”below).

Since a film thickness trend, an average value of film thicknesses, anda film thickness dispersion (a sum of squared residuals of a filmthickness) are all dependent on refractive index n₁, film thicknessdispersion D(n₁) of film thickness d₁(j) can be defined as a costfunction as in a formula (14) below.

$\begin{matrix}{{D\left( n_{1} \right)} = {\frac{B_{y}}{C_{y}}{\sum\limits_{j = 1}^{C_{y}\text{/}B_{y}}\;\left\{ {{d_{1}\left( {n_{1},j} \right)} - {\overset{\_}{d_{1}}\left( n_{1} \right)}} \right\}^{2}}}} & (14)\end{matrix}$

In the formula (14) above, refractive index n₁ under the condition thatfilm thickness dispersion D(n₁) is minimized, that is, a condition of∂D/∂n₁=0 is satisfied, can be found by sequentially varying a value ofrefractive index n₁.

FIGS. 23A and 23B are graphs showing examples of film thickness trendscalculated in accordance with the refractive index measurement method(No. 1) based on information in the wavelength direction according tothe present embodiment. The graph in FIG. 23A shows the film thicknesstrend for each refractive index n₁ (constant value) of a polyethylenethin film. For facilitation of comparison of variation in film thicknesstrend, the graph in FIG. 23B shows a result of such standardization asachieving film thickness d₁=10 [μm] at position-direction pixel numberj=600. In calculating the film thickness trends in FIGS. 23A and 23B, atheoretical value of transmittance spectrum T(λ) used in generating thetwo-dimensional image shown in FIG. 15 described above was used.

It can be seen that, with increase in refractive index n₁ of sample Sfrom 1.51 in increments of 0.01, the film thickness trend varies fromdownwardly projecting to upwardly projecting since increase from 1.56 to1.57. It can be seen that, when refractive index n₁ is set to 1.56, filmthickness dispersion D(n₁) is minimized and the film thickness trend isalso flattest. A table below shows values involved with the filmthickness trends shown in FIGS. 23A and 23B.

TABLE 1 Average Value Film Refractive of Film Thick- Thickness Index n₁ness d1 (n₁) Dispersion D(n₁) 1.51 10.232 5.072 × 10⁻⁶ 1.52 10.165 3.271× 10⁻⁶ 1.53 10.098 1.815 × 10⁻⁶ 1.54 10.031 9.265 × 10⁻⁷ 1.55 9.9673.240 × 10⁻⁷ 1.56 9.902 5.609 × 10⁻⁸ 1.57 9.838 9.641 × 10⁻⁸ 1.58 9.7763.981 × 10⁻⁷ 1.59 9.714 9.365 × 10⁻⁷

When refractive index n₁ is calculated with accuracy of 1/100 fromresults of calculation as above, refractive index n₁ can be determinedas 1.56.

Though the formulae (12), (13), and (14) above are written to use all ofposition-direction pixel numbers j in calculation of film thicknessdispersion D(n₁), all of them do not necessarily have to be used, and aprescribed number of pixel rows may be used in accordance with requiredaccuracy. In this case, measurement points at which sample S is arrangedshould also be arranged at intervals greater than a resolution in thefilm thickness measurement method.

FIG. 24 is a flowchart showing a processing procedure in the refractiveindex measurement method (No. 1) based on information in the wavelengthdirection according to the present embodiment. Referring to FIG. 24,initially, a user repeats arrangement of a small piece of sample S ateach measurement point on the measurement line and obtainment of anactually measured value from arranged sample S by operating opticalmeasurement apparatus 1 (step S200). Processing device 100 thus obtainstransmittance distribution T_(meas)(i, j) (or reflectance distributionR_(meas)(i, j)) measured for the same sample S.

In succession, processing device 100 calculates angle of incidence θ₀corresponding to each measurement point, of measurement interferencelight incident on measurement optical system 10 (step S202). Then,processing device 100 calculates wavelength conversion formula λ(i, j)representing relation between a pixel position in two-dimensional image150 and wavelength λ from a result of wavelength calibration formeasurement optical system 10 (step S204).

Since processing in steps S202 and S204 is the same as in steps S100 andS104 in the flowchart of the processing procedure (No. 1) in the filmthickness measurement method shown in FIG. 11, detailed description willnot be repeated.

In succession, processing device 100 sets refractive index n₁ to anyinitial value (step S206). Then, processing device 100 calculates filmthicknesses d₁(j) from transmittance distribution T_(meas)(i, j) (orreflectance distribution R_(meas)(i, j)) at a plurality ofposition-direction pixel numbers j (step S208).

Processing device 100 calculates an average value of calculated filmthicknesses d₁(j) (step S210) and calculates film thickness dispersionD(n₁) by using the average value of the film thicknesses calculated instep S210 (step S212). Processing device 100 then determines whether ornot variation in refractive index n₁ within a predetermined range hasbeen completed (step S214). When variation in refractive index n₁ withinthe predetermined range has not been completed (NO in step S214),processing device 100 updates refractive index n₁ (step S216) andrepeats processing in step S208 or later.

When variation in refractive index n₁ within the predetermined range hasbeen completed (YES in step S214), processing device 100 determines aminimum film thickness dispersion of film thickness dispersions D(n₁)calculated in step S212 (step S218) and determines refractive index n₁corresponding to determined film thickness dispersion D(n₁) as arefractive index of sample S (step S220). Then, the process ends.Refractive index n₁ at which calculated film thickness dispersion D(n₁)becomes small is determined as a refractive index of sample S.

Refractive index n₁ of sample S can be determined based on theinformation in the wavelength direction as above.

(f3: Refractive Index Measurement Method (No. 2) Based on Information inWavelength Direction)

Though a method of analytically determining refractive index n₁ ofsample S is exemplified in the refractive index measurement method(No. 1) based on the information in the wavelength direction describedabove, refractive index n₁ may be determined by fitting by using apredetermined polynomial.

FIG. 25 is a diagram for illustrating a method of determining refractiveindex n₁ in the refractive index measurement method (No. 2) based on theinformation in the wavelength direction according to the presentembodiment. FIG. 25 shows a graph in which film thickness dispersionD(n₁) calculated at the time of variation in refractive index n₁ isplotted. For example, a cubic polynomial as shown in a formula (15)below can be fitted to relation between refractive index n₁ and filmthickness dispersion D(n₁) as shown in FIG. 25.

Coefficients A₃, A₂, A₁, and A₀ in the formula (15) are fitted to passthrough film thickness dispersion D(n₁) shown in FIG. 25. Refractiveindex n₁ can be determined in correspondence with a point where thecubic polynomial fitted as shown in FIG. 25 takes a relative minimumvalue (a minimum value). Refractive index n₁ can be calculated based oncoefficients A₃, A₂, A₁, and A₀ in accordance with a formula (16) below.

$\begin{matrix}{D = {{A_{3}x^{3}} + {A_{2}x^{2}} + {A_{1}x} + A_{0}}} & (15) \\{n_{1} = \frac{{- A_{2}} + \sqrt{A_{2}^{2} - {3A_{3}A_{1}}}}{3A_{3}}} & (16)\end{matrix}$

Table 2 below shows results obtained by fitting shown in FIG. 25.

TABLE 2 D = A₃x³ + A₂x² + A₁x¹ + A₀ Refractive A₃ A₂ A₁ A₀ Index n₁−0.006408 0.031479 −0.051442 0.027969 1.5634

When refractive index n₁ is calculated with accuracy of 1/10000 fromresults of calculation as above, refractive index n₁ can be determinedas 1.5634. A refractive index can be determined with accuracy higherthan variation in refractive index n₁ (in this example, in increments of0.01 (that is, accuracy of 1/100)).

A refractive index of sample S can be determined by fitting a polynomialrepresenting a predetermined film thickness dispersion to relationbetween a refractive index and a film thickness dispersion, based on apoint at which the film thickness dispersion represented by thepolynomial determined by fitting takes an extreme value.

In the processing procedure in the refractive index measurement method(No. 2) based on the information in the wavelength direction, fittingwith the polynomial as shown in FIG. 25 is performed instead of stepsS218 and S220 in the flowchart shown in FIG. 24. Since the processingprocedure is otherwise the same as in the refractive index measurementmethod (No. 1) based on the information in the wavelength directiondescribed above, detailed description will not be repeated.

(f4: Refractive Index Measurement Method (No. 3) Based on Information inWavelength Direction)

Refractive index n₁ of sample S can more efficiently be determined bypaying attention to information affected more by angle of incidence θ₀of the information in the wavelength direction as described above. Morespecifically, initially, a squared residual value y(n₁, j) representinga deviation from an average value of film thicknesses d₁(j) at anyposition-direction pixel number j is defined as shown in a formula (17)below.y(n ₁ ,j)≡{d ₁(n ₁ ,j)− d ₁ (n ₁)}²  (17)

FIG. 26 is a diagram for illustrating a method of determining refractiveindex n₁ in the refractive index measurement method (No. 3) based oninformation in the wavelength direction according to the presentembodiment. FIG. 26 shows a graph in which squared residual value ycalculated at the time of variation in refractive index n₁ is plotted.For example, the cubic polynomial as shown in the formula (15) above canbe fitted to relation between refractive index n₁ and squared residualvalue y as shown in FIG. 26.

Coefficients A₃, A₂, A₁, and A₀ in the formula (15) are fitted to passthrough squared residual value y shown in FIG. 26. Refractive index n₁can be determined in correspondence with a point where the cubicpolynomial fitted as shown in FIG. 26 takes a relative minimum value (aminimum value). Refractive index n₁ can be calculated based oncoefficients A₃, A₂, A₁, and A₀ in accordance with the formula (16)above.

Table 3 below shows results obtained by fitting shown in FIG. 26.

TABLE 3 y = A₃x³ + A₂x² + A₁x¹ + A₀ Refractive j A₃ A₂ A₁ A₀ Index n₁ 50−0.018765 0.091930 −0.149815 0.081228 1.5587 100 −0.008182 0.040403−0.066308 0.036179 1.5570 1100 −0.010970 0.053523 −0.086941 0.0470201.5690 1150 −0.013067 0.065614 −0.109397 0.060590 1.5694 Average of n₁1.5636

In the table above, refractive index n₁ was calculated at fourposition-direction pixel numbers (j=50, 100, 1100, 1150) where angle ofincidence θ₀ is expected to be relatively large.

In the refractive index measurement method (No. 3) based on theinformation in the wavelength direction according to the presentembodiment, a spectrum should be measured by arranging sample S at atleast two measurement points. Therefore, time and efforts formeasurement can be lessened and refractive index n₁ can be calculated ina simplified manner. Positions where a difference in angle of incidenceis great are preferably selected as measurement points where sample S isto be arranged.

Refractive index n₁ can also be calculated from a point where squaredresidual value y takes a relative minimum value (minimum value) withattention being paid to specific position-direction pixel number j wherean angle of incidence is as large as possible. For example, whenrefractive index n₁ is calculated with accuracy of 1/10000 atposition-direction pixel number j=50 in the table above, refractiveindex n₁ can be determined as 1.5587. By using a polynomial for fitting,a refractive index can be determined with accuracy higher than variationin refractive index n₁ (in this example, in increments of 0.01 (that is,accuracy of 1/100)).

A refractive index of sample S can be determined by thus fitting apolynomial representing a predetermined squared residual value torelation between refractive index n₁ and a squared residual value foreach calculated film thickness, based on a point where the squaredresidual value expressed by the polynomial determined by fitting takesan extreme value.

The processing procedure in the refractive index measurement method (No.3) based on the information in the wavelength direction is differentfrom the processing procedure in the refractive index measurement method(No. 2) based on the information in the wavelength direction describedabove only in use of squared residual value y instead of film thicknessdispersion D(n₁). Since the processing procedure is otherwise the sameas in the refractive index measurement method (No. 1) based on theinformation in the wavelength direction described above, detaileddescription will not be repeated.

(f5: Refractive Index Measurement Method (No. 4) Based on Information inWavelength Direction)

In the description of the refractive index measurement method (No. 1)based on the information in the wavelength direction described above, acondition of refractive index n₁(λ)=n₁ (constant value) was assumed. Inactual, however, refractive index n₁(λ) is wavelength-dependent. In thiscase, refractive index n₁(λ) is defined with a high-order formula andeach coefficient in the high-order formula is to be fitted, so thatrefractive index n₁(λ) in consideration of wavelength-dependency can bedetermined.

By way of example, a Cauchy dispersion formula as shown in a formula(18) below may be used. Coefficients (E, F, G) in terms in the formula(18) are varied, and a set of coefficients with which a value to beevaluated (film thickness dispersion D(n₁) in the refractive indexmeasurement method (No. 2) based on the information in the wavelengthdirection described above) takes a relative minimum value (a minimumvalue) should be determined with the least squares method.

In a formula (19) below in which film thickness dispersion D isdependent on coefficients (E, F, G), a set of coefficients (E, F, G)satisfying a condition of ∂D/∂E=∂D/∂F=∂D/∂G=0 is found, so thatrefractive index n₁(λ) in consideration of wavelength-dependency can befound based on the formula (18).

$\begin{matrix}{{n_{1}(\lambda)} = {E + \frac{F}{\lambda^{2}} + \frac{G}{\lambda^{4}}}} & (18) \\{{D\left( {E,F,G} \right)} = {\frac{B_{y}}{C_{y}}{\sum\limits_{j = 1}^{C_{y}\text{/}B_{y}}\;\left\{ {{d_{1}\left( {E,F,G,j} \right)} - {\overset{\_}{d_{1}}\left( {E,F,G} \right)}} \right\}^{2}}}} & (19)\end{matrix}$

Though refractive index n₁ is calculated from a point where squaredresidual value y takes a relative minimum value (a minimum value) in therefractive index measurement method (No. 3) based on the information inthe wavelength direction described above, refractive index n₁(λ) inconsideration of wavelength-dependency can be found also with thismethod. Refractive index n₁(λ) in consideration of wavelength-dependencycan be found from the formula (18) by deriving y(D, E, F) as in theformula (19) above and finding a set of coefficients (E, F, G)satisfying a condition of ∂y/∂E=∂y/∂F=∂y/∂G=0.

A refractive index of sample S can be determined by thus calculating arefractive index of sample S in accordance with a prescribed wavelengthdispersion formula and applying the least squares method to any ofrelation between each coefficient defining the wavelength dispersionformula and a film thickness dispersion and relation between eachcoefficient defining the wavelength dispersion formula and the squaredresidual value, based on a set of coefficients at the time when the filmthickness dispersion or the squared residual value takes an extremevalue.

Refractive index n₁(λ) in consideration of wavelength-dependency can befound in the procedure as above.

(f6: Refractive Index Measurement Method (No. 1) Based on Information inPosition Direction)

The refractive index measurement method based on information in theposition direction will now be described. As described with reference toFIG. 22 above, in measurement of refractive index n₁ of sample S basedon information in the position direction, refractive index n(i) isdetermined by comparing a trend along position-direction pixel number jfor one wavelength-direction pixel number i or a plurality ofwavelength-direction pixel numbers i, in connection with transmittancedistribution T_(meas)(i, j) (or reflectance distribution R_(meas)(i, j))measured for a small piece of the same sample S and transmittancedistribution T_(theo)(i, j, n₁(i)) (or reflectance distributionR_(theo)(i, j, n₁(i))) calculated in accordance with a functionincluding refractive index n₁.

Initially, for sample S (having film thickness d₁) of a thin film in air(medium 0) as shown in FIGS. 7A and 7B described above, transmittancedistribution T_(theo) in consideration of multiple reflection in sampleS is as shown in a formula (20) below. Refractive index n₀ of air isdefined as n₀=1.

$\begin{matrix}{{T_{theo}\left( {i,j,d_{1},{n_{i}(i)}} \right)} = \frac{\left( {1 - r_{01}^{2}} \right)^{2}}{1 + r_{01}^{4} - {2r_{01}^{2}\mspace{14mu}\cos\left\{ {\frac{4\pi\; d_{1}}{\lambda(i)}\sqrt{{n_{1}(i)}^{2} - {\sin^{2}\mspace{14mu}{\theta_{0}(j)}}}} \right\}}}} & (20)\end{matrix}$

In the formula (20) above, amplitude reflectance r₀₁ is expressed as ina formula (21-1) below, for each of s polarization and p polarization.Since relation of n₀·sin θ₀=n₁·sin θ₁ (Snell's law) is satisfied betweenangle of incidence θ₀ and angle of refraction θ₁, the formula (21-1) canbe deformed as in a formula (21-2). Refractive index n₀ of air isdefined as n₀=1. Amplitude reflectance r₀₁ can be defined only byrefractive index n₁ of sample S and angle of incidence θ₀.

$\begin{matrix}\left. \begin{matrix}{r_{01}^{s} = \frac{{n_{0}\mspace{14mu}\cos\mspace{14mu}\theta_{0}} - {n_{1}\mspace{14mu}\cos\mspace{14mu}\theta_{1}}}{{n_{0}\mspace{14mu}\cos\mspace{14mu}\theta_{0}} + {n_{1}\mspace{14mu}\cos\mspace{14mu}\theta_{1}}}} \\{r_{01}^{p} = \frac{{n_{1}\mspace{14mu}\cos\mspace{14mu}\theta_{0}} - {n_{0}\mspace{14mu}\cos\mspace{14mu}\theta_{1}}}{{n_{1}\mspace{14mu}\cos\mspace{14mu}\theta_{0}} + {n_{0}\mspace{14mu}\cos\mspace{14mu}\theta_{1}}}}\end{matrix} \right\} & \left( {21\text{-}1} \right) \\\left. \begin{matrix}{{r_{01}^{s} = \frac{{\cos\mspace{14mu}\theta_{0}} - \sqrt{n_{1}^{2} - {\sin^{2}\mspace{14mu}\theta_{0}}}}{{\cos\mspace{14mu}\theta_{0}} + \sqrt{n_{1}^{2} - {\sin^{2}\mspace{14mu}\theta_{0}}}}}\mspace{34mu}} \\{r_{01}^{p} = \frac{{n_{1}^{2}\mspace{14mu}\cos\mspace{14mu}\theta_{0}} - \sqrt{n_{1}^{2} - {\sin^{2}\mspace{14mu}\theta_{0}}}}{{n_{1}^{2}\mspace{14mu}\cos\mspace{14mu}\theta_{0}} + \sqrt{n_{1}^{2} - {\sin^{2}\mspace{14mu}\theta_{0}}}}}\end{matrix} \right\} & \left( {21\text{-}2} \right)\end{matrix}$

Since an intensity reflectance R₀₁=|r₀₁|² when no polarization occursincludes components of both of s polarization and p polarization,definition as in a formula (22) below can be made.

$\begin{matrix}{\left| r_{01} \right|^{2} = \frac{\left| r_{01}^{s} \middle| {}_{2}{+ \left| r_{01}^{p} \right|^{2}} \right.}{2}} & (22)\end{matrix}$

By substituting the formula (21-1) and the formula (22) into the formula(20) above to cancel amplitude reflectance r₀₁, transmittancedistribution T_(theo) can be defined by refractive index n₁(i) of sampleS, angle of incidence θ₀(j), film thickness d₁ of sample S, andwavelength λ(i).

As described above, transmittance distribution T_(meas)(i, j) (orreflectance distribution R_(meas)(i, j)) is represented as a valuemeasured by arranging a small piece of the same sample S at eachmeasurement point on the measurement line, and film thickness d₁ takes aconstant value without depending on wavelength-direction pixel number iand position-direction pixel number j.

With attention being paid to specific wavelength-direction pixel numberi, a sum of squared residuals Q representing an error betweentransmittance distribution T_(meas)(i, j) (or reflectance distributionR_(meas)(i, j)) and transmittance distribution T_(meas)(i, j) (orreflectance distribution R_(meas)(i, j)) can be defined as in a formula(23) below.

$\begin{matrix}{{Q\left( {i,d_{1},{n_{i}(i)}} \right)} = {\frac{B_{y}}{C_{y}}{\sum\limits_{j = 1}^{C_{y}\text{/}B_{y}}\;\left\{ {{T_{theo}\left( {i,j,d_{1},{n_{1}(i)}} \right)} - {T_{meas}\left( {i,j} \right)}} \right\}^{2}}}} & (23)\end{matrix}$

By satisfying a condition minimizing sum of squared residuals Q definedin the formula (23) above, that is, a condition of ∂Q/∂d₁=∂Q/∂n₁(i)=0,refractive index n₁(i) at wavelength-direction pixel number i ofinterest and corresponding film thickness d₁ can be determined.

Since film thickness d₁ takes a constant value without depending onwavelength-direction pixel number i and position-direction pixel numberj, refractive index n₁(i) calculated at one wavelength-direction pixelnumber i and corresponding film thickness d₁ may be output as finalvalues when wavelength-dependency of refractive index n₁ is not takeninto consideration (that is, when refractive index n₁ is constant).

In order to further enhance accuracy in measurement, a set of refractiveindex n₁ and film thickness d₁ may be determined for allwavelength-direction pixel numbers i. In this case, a result ofstatistical processing such as averaging of values of sets of refractiveindex n₁ and film thickness d₁ may finally be output.

As will be described in the refractive index measurement method (No. 3)based on the information in the position direction which will bedescribed later, when wavelength-dependency of refractive index n₁ istaken into consideration, a plurality of wavelength-direction pixelnumbers i should be considered.

Though the formula (23) above is written to use all ofposition-direction pixel numbers j in calculation of sum of squaredresiduals Q, all of them do not necessarily have to be used, and aprescribed number of pixel rows may be used in accordance with requiredaccuracy. In this case, measurement points at which sample S is arrangedshould also be arranged at intervals greater than a resolution in thefilm thickness measurement method.

Since the processing procedure in the refractive index measurementmethod (No. 1) based on the information in the position direction is thesame as the processing procedure in the refractive index measurementmethod (No. 1) based on the information in the wavelength directionshown in FIG. 24 except for a function of a sum of squared residuals,detailed description will not be repeated.

Thus, in the present measurement method, a distribution of actuallymeasured values represented by a group of pixel values in the positiondirection for any wavelength in the distribution of the actuallymeasured values is calculated, and a distribution of theoretical valuesfor any wavelength is calculated based on a film thickness and arefractive index of a sample which are set in advance and a modificationfactor corresponding to each position. Then, a film thickness and arefractive index of the sample are determined so as to make an errorbetween the distribution of the theoretical values and the distributionof the actually measured values smaller. A refractive index of thesample may be determined for each of a plurality of wavelengths in thedistribution of the actually measured values.

(f7: Refractive Index Measurement Method (No. 2) Based on Information inPosition Direction)

In the refractive index measurement method (No. 1) based on theinformation in the position direction described above, refractive indexn₁ and film thickness d₁ are determined for each wavelength-directionpixel number i by comparing an actually measured value and a theoreticalvalue with each other.

In the refractive index measurement method (No. 2) based on informationin the position direction, refractive index n₁ is more highly accuratelydetermined by applying such advance information as film thickness d₁being the same. More specifically, a flatness of a film thickness trendmay be adopted as a cost function, and refractive index n₁ at which avalue of the cost function is minimized may be determined. A filmthickness trend curve d₁(i) at the time of variation inwavelength-direction pixel number i is approximated to a constantfunction f(j)=μ (μ being a constant value). A sum of squared residuals Scan be defined as in a formula (24) below. Constant value μ in theformula (24) is determined with the least squares method. Morespecifically, a formula (25) below is obtained by finding constant valueμ under such a condition that sum of squared residuals S is minimized,that is, a condition of ∂S/∂μ=0 is satisfied.

$\begin{matrix}{S = {\sum\limits_{i = 1}^{C_{x}\text{/}B_{x}}\left\{ {{d_{1}(i)} - \mu} \right\}^{2}}} & (24) \\{\mu = {{\frac{B_{x}}{C_{x}}{\sum\limits_{i = 1}^{C_{x}\text{/}B_{x}}{d_{1}(i)}}} \equiv \overset{\_}{d_{1}}}} & (25)\end{matrix}$

Constant value μ calculated in accordance with the formula (25)corresponds to an average value of film thicknesses d₁(i). Since sum ofsquared residuals S is a sum of squared residuals of the average valueof film thicknesses d₁(i), it corresponds to a dispersion of filmthicknesses d₁(i) (which is also referred to as a “film thicknessdispersion” below).

FIG. 27 is a diagram for illustrating a method of determining a moreprobable value of film thickness d₁ in the refractive index measurementmethod (No. 2) based on information in the position direction accordingto the present embodiment. Though film thicknesses d₁ as many aswavelength-direction pixel numbers i can be calculated, film thicknessesd₁ calculated for wavelength-direction pixel numbers i should be equalin value to one another. As shown in FIG. 27, film thickness trend curved₁(i) at the time of variation in wavelength-direction pixel number i isapproximated to a constant function f(i)=μ (μ being a constant value).Constant μ is then determined such that sum of squared residuals Sbetween d₁(i) and f(i) takes a relative minimum value (a minimum value).Constant μ thus determined represents a more probable film thickness d₁.

More probable film thickness d₁=μ is given to a term representing atheoretical value of a transmittance in the formula (25), and sum ofsquared residuals Q between the theoretical value of the transmittanceand an actually measured value of the transmittance is defined as in aformula (26) below.

$\begin{matrix}{{Q\left( {i,\mu,{n_{i}(i)}} \right)} = {\frac{B_{y}}{C_{y}}{\sum\limits_{j = 1}^{C_{y}\text{/}B_{y}}\left\{ {{T_{theo}\left( {i,j,\mu,{n_{1}(i)}} \right)} - {T_{meas}\left( {i,j} \right)}} \right\}^{2}}}} & (26)\end{matrix}$

By satisfying a condition that sum of squared residuals Q defined in theformula (26) above is minimized, that is, a condition of ∂Q/∂n₁(i)=0 issatisfied, refractive index n₁(i) at wavelength-direction pixel number iof interest and corresponding film thickness d₁ can be determined.

Since film thickness d₁ has a constant value without depending onwavelength-direction pixel number i and position-direction pixel numberj as described above, refractive index n₁(i) calculated for onewavelength-direction pixel number i and corresponding film thickness d₁may be output as final values when wavelength-dependency of refractiveindex n₁ is not taken into consideration (that is, when refractive indexn₁ has a constant value).

In order to further enhance accuracy in measurement, a set of refractiveindex n₁ and film thickness d₁ may be determined for allwavelength-direction pixel numbers i. In this case, a result ofstatistical processing such as averaging of values of sets of refractiveindex n₁ and film thickness d₁ may finally be output.

As will be described in the refractive index measurement method (No. 3)based on the information in the position direction which will bedescribed later, when wavelength-dependency of refractive index n₁ istaken into consideration, a plurality of wavelength-direction pixelnumbers i should be considered.

Though the formula (26) above is written to use all ofposition-direction pixel numbers j in calculation of sum of squaredresiduals Q, all of them do not necessarily have to be used, and aprescribed number of pixel rows may be used in accordance with requiredaccuracy. In this case, measurement points at which sample S is arrangedshould also be arranged at intervals greater than a resolution in thefilm thickness measurement method.

Since the processing procedure in the refractive index measurementmethod (No. 1) based on the information in the position direction is thesame as the processing procedure in the refractive index measurementmethod (No. 1) based on the information in the wavelength directionshown in FIG. 24, detailed description will not be repeated.

Thus, in the present measurement method, film thicknesses of a sampleare calculated for a plurality of wavelengths in a distribution ofactually measured values based on an error between a distribution oftheoretical values and a distribution of actually measured values, and amore probable film thickness is determined based on the calculated filmthicknesses.

(f8: Refractive Index Measurement Method (No. 3) Based on Information inPosition Direction)

In the description of the refractive index measurement methods (Nos. 1and 2) based on information in the position direction described above,an example in which a condition of refractive index n₁(λ)=n₁ (constantvalue) is satisfied is assumed. In actual, however, refractive indexn₁(λ) is wavelength-dependent. In this case, refractive index n₁(λ) isdefined with a high-order formula and each coefficient in the high-orderformula is to be fitted, so that refractive index n₁(λ) in considerationof wavelength-dependency can be determined.

By way of example, the Cauchy dispersion formula as shown in the formula(18) above may be used. In this case, coefficients (E, F, G) in terms inthe formula (18) can be determined by calculating refractive index n₁(i)at at least three points at wavelength-direction pixel number i.

In using the Cauchy dispersion formula, a plurality of data rows in theposition direction at each wavelength-direction pixel number i can alsocollectively be handled. Namely, film thickness d₁ and the coefficients(E, F, G) for a plurality of different wavelength-direction pixelnumbers i can be handled as common parameters without depending onwavelength-direction pixel number i, and the coefficients (E, F, G) canbe determined such that sum of squared residuals Q including also thesum for the plurality of wavelength-direction pixel numbers i inaddition to position-direction pixel number j is minimized when thesefour parameters are varied.

More specifically, a set of film thickness d₁ and the coefficients (E,F, G) which satisfies a condition of ∂Q/∂d₁=∂Q/∂E=∂Q/∂F=∂Q/∂G=0 may befound. The Gauss-Newton method, the steepest descent method, and theLevenberg-Marquardt method can be used for an algorithm in this case.

In yet another method, wavelength-dependency n₁(λ) of the refractiveindex can also be determined by applying the least squares method to theformula (26) above, calculating refractive index n₁(i) for eachwavelength-direction pixel number i, and thereafter aggregatingrefractive index n₁(i) (i=1, 2, 3, . . . , C_(x)/B_(x)) for eachcalculated wavelength-direction pixel number i. In this method, it isnot necessary to particularly designate a form of a function (a modelformula) of wavelength-dependency of the refractive index.

In the procedure as above, refractive index n₁(λ) in consideration ofwavelength-dependency can be found.

Thus, the present measurement method is set such that a refractive indexof a sample used for calculation of a distribution of theoretical valuesis calculated in accordance with a prescribed wavelength dispersionformula. Then, each coefficient defining the prescribed wavelengthdispersion formula and a film thickness are fitted to make smaller,errors between the distribution of the theoretical values and thedistribution of the actually measured values for a plurality ofwavelengths in the distribution of the actually measured values.

G. Application Examples

Application examples of the optical measurement apparatus according tothe present embodiment will now be described.

For example, by being arranged in a film manufacturing line, the opticalmeasurement apparatus according to the present embodiment can conductin-line measurement of a film thickness. The optical measurementapparatus according to the present embodiment can output an in-planefilm thickness distribution (that is, a two-dimensional film thicknessdistribution) of a sample. For example, a defective portion which may beproduced in the film manufacturing line can also be specified based onvariation in film thickness trend in a direction of transportation, thatis, a machine direction (MD), of the sample.

More specifically, for example, the film manufacturing line includes aplurality of transportation rollers and any transportation rollercontains a defective portion such as formation of a projecting portionin the film or introduction of a foreign matter into a surface of theroller. In this case, it is expected that a film thickness is variedwith a period dependent on a radius (or a length of a circumference) ofthe transportation roller or a length of a film wound around thetransportation roller. A defective portion in the film manufacturingline can be specified based on periodicity of variation produced in sucha film thickness trend in the MD direction (variation in film thickness,production of streaks or unevenness, or production of local unevenness).

Inspection for a defect can thus be conducted by making use ofperiodicity of a film thickness trend output by the optical measurementapparatus according to the present embodiment.

The optical measurement apparatus according to the present embodimentcan be used for any application without being limited to theapplications as described above.

For example, a semiconductor, a function film, plastics, and variousfilters are subjected to in-line measurement of a film thickness.

H. Other Embodiments

(h1: Determination of Angle of View and Position of Center Based onActually Measured Film Thickness Value)

The description above is on the premise that angle of view ϕ(=Atan(b/2f)) of measurement optical system 10 is theoreticallydetermined by length b of imaging device 160 and focal length f ofobject lens 12 based on catalogue specifications.

Depending on a type of object lens 12 to actually be used, however, aneffective focal length f′ may slightly deviate from a catalogue value offocal length f due to distortion of the lens or variation in focusing.It is also expected that it is slightly difficult to match a position ofthe center of a pixel (j=C_(y)/2B_(y)) and the center of imaging byimaging portion 16 with each other in optical adjustment.

In such a case, the effective value of the angle of view and theposition of the center may be determined based on an actually measuredvalue of the film thickness. For example, a transmittance spectrum or areflectance spectrum in the wavelength direction when position-directionpixel number j (that is, angle of incidence θ₀) is different for thesame sample S is measured. Then, the film thickness is calculated inaccordance with the processing procedure (No. 1) in the film thicknessmeasurement method described above without correcting angle of incidenceθ₀ for the measured transmittance spectrum or reflectance spectrum.Through such a procedure, a film thickness trend representing variationin film thickness corresponding to each measurement point can beobtained.

By fitting the obtained film thickness trend with a function such asy=cosA(x−x0) after standardizing a value of the film thickness at theposition of the center of a pixel to 1, an effective angle of view ϕ′(=Atan(b/2f′)) and a position of the center x₀ can be calculated basedon the actually measured value of the film thickness.

(h2: Parallel Arrangement of a Plurality of Optical MeasurementApparatuses)

When the optical measurement apparatus according to the presentembodiment is arranged in a film manufacturing line, a plurality ofoptical measurement apparatuses according to the present embodiment arearranged in parallel in accordance with a width of the line for thefilm. In such a case, a portion overlapping with a range of measurementby another adjacently arranged measurement optical system 10 may becreated around an end portion of the range of measurement by measurementoptical system 10. Namely, it is expected that the same point in sampleS is included in a plurality of ranges of measurement by measurementoptical system 10. In such a case, results of measurement for the samepoint in sample S output from the optical measurement apparatuses may bedifferent from each other. Since such inconsistency is not preferred inmanagement of the line, results of measurement may be matched byadopting a modification method as below.

In the optical measurement apparatus according to the presentembodiment, influence by an angle of incidence of measurementinterference light can be eliminated. Therefore, a film thicknesscalculated for the same point in a sample is constant regardless of theangle of incidence. For example, a film thickness of a small piece (forexample, of a 1-mm square) of the same sample S may be measured with theoptical measurement apparatuses, and offset modification and/or acoefficient may be set for the optical measurement apparatuses such thatmeasured film thicknesses (for example, measurement values atmeasurement points at which the angle of incidence is zero) areconsistent.

I. Advantages

As described above, according to the present embodiment, an in-planefilm thickness distribution of various samples can be measured fasterand more accurately. According to the present embodiment, opticalcharacteristics of a sample such as a refractive index can be measuredwithout using a dedicated measurement apparatus.

Though embodiments of the present invention have been described, itshould be understood that the embodiment disclosed herein isillustrative and non-restrictive in every respect. The scope of thepresent invention is defined by the terms of the claims and is intendedto include any modifications within the scope and meaning equivalent tothe terms of the claims.

What is claimed is:
 1. An optical measurement method with an opticalmeasurement apparatus including an irradiation optical system and ameasurement optical system, the irradiation optical system beingconfigured to linearly irradiate a measurement target with measurementlight having a certain wavelength range, the measurement optical systembeing configured to output a two-dimensional image by expanding linearmeasurement interference light in a wavelength direction orthogonal to alongitudinal direction of the measurement interference light, themeasurement interference light being transmitted light or reflectedlight originating from the measurement target as a result of irradiationwith the measurement light, the optical measurement method comprising:obtaining a distribution of actually measured values when angles ofincidence are different for an identical sample; calculating amodification factor depending on an angle of incidence on themeasurement optical system from each measurement point in associationwith a region in the two-dimensional image corresponding to eachmeasurement point in the measurement target irradiated with themeasurement light; and calculating optical characteristics including arefractive index of the sample based on a group of pixel values in onerow or a plurality of rows along any one direction in the distributionof the actually measured values and corresponding modification factors.2. The optical measurement method according to claim 1, wherein thecalculating optical characteristics includes calculating filmthicknesses at a plurality of positions in the distribution of theactually measured values based on a set refractive index, a modificationfactor corresponding to each position, and a group of pixel values in awavelength direction at each position, calculating a film thicknessdispersion which is a dispersion of the calculated film thicknesses,repeating the calculating film thicknesses and the calculating a filmthickness dispersion, with the refractive index of the sample being setto a plurality of different values, and determining a refractive indexof the sample based on the calculated film thickness dispersion.
 3. Theoptical measurement method according to claim 2, wherein the determininga refractive index of the sample includes determining a refractive indexat which the calculated film thickness dispersion becomes small as arefractive index of the sample.
 4. The optical measurement methodaccording to claim 2, wherein the determining a refractive index of thesample includes fitting a polynomial representing a predetermined filmthickness dispersion to relation between a refractive index and a filmthickness dispersion, and determining a refractive index of the samplebased on a point at which the film thickness dispersion represented bythe polynomial determined by fitting takes an extreme value.
 5. Theoptical measurement method according to claim 2, wherein the determininga refractive index of the sample includes fitting a polynomialrepresenting a predetermined squared residual value to relation betweena refractive index and a squared residual value for the calculated filmthicknesses, and determining a refractive index of the sample based on apoint at which the squared residual value represented by the polynomialdetermined by fitting takes an extreme value.
 6. The optical measurementmethod according to claim 2, wherein a refractive index of the sample iscalculated in accordance with a prescribed wavelength dispersionformula, and the determining a refractive index of the sample includesapplying a least squares method to any of relation between eachcoefficient defining the wavelength dispersion formula and a filmthickness dispersion and relation between each coefficient defining thewavelength dispersion formula and a squared residual value, anddetermining a refractive index of the sample based on a set ofcoefficients when the film thickness dispersion or the squared residualvalue takes an extreme value.
 7. The optical measurement methodaccording to claim 1, wherein the calculating optical characteristicsincludes calculating a distribution of actually measured valuesexhibited by a group of pixel values in a position direction for anywavelength in the distribution of the actually measured values,calculating a distribution of theoretical values for the any wavelengthbased on a film thickness and a refractive index of the sample that areset in advance and a modification factor corresponding to each position,and determining a film thickness and a refractive index of the sample soas to decrease an error between the distribution of the theoreticalvalues and the distribution of the actually measured values.
 8. Theoptical measurement method according to claim 7, wherein the calculatingoptical characteristics includes determining a refractive index of thesample for each of a plurality of wavelengths in the distribution of theactually measured values.
 9. The optical measurement method according toclaim 7, wherein the calculating optical characteristics includescalculating film thicknesses of the sample for a plurality ofwavelengths in the distribution of the actually measured values based onthe error between the distribution of the theoretical values and thedistribution of the actually measured values, and determining a moreprobable film thickness based on the calculated film thicknesses. 10.The optical measurement method according to claim 7, wherein therefractive index of the sample used for calculation of the distributionof the theoretical values is calculated in accordance with a prescribedwavelength dispersion formula, and the calculating opticalcharacteristics includes fitting each coefficient defining theprescribed wavelength dispersion formula and the film thickness so as todecrease errors between the distribution of the theoretical values andthe distribution of the actually measured values for a plurality ofwavelengths in the distribution of the actually measured values.
 11. Anoptical measurement apparatus comprising: an irradiation optical systemconfigured to linearly irradiate a measurement target with measurementlight having a certain wavelength range; a measurement optical systemconfigured to output a two-dimensional image by expanding linearmeasurement interference light in a wavelength direction orthogonal to alongitudinal direction of the measurement interference light, themeasurement interference light being transmitted light or reflectedlight originating from the measurement target as a result of irradiationwith the measurement light; and a processing device configured to obtaina distribution of actually measured values when angles of incidence aredifferent for an identical sample, calculate a modification factordepending on an angle of incidence on the measurement optical systemfrom each measurement point in association with a region in thetwo-dimensional image corresponding to each measurement point in themeasurement target irradiated with the measurement light, and calculateoptical characteristics including a refractive index of the sample basedon a group of pixel values in one row or a plurality of rows along anyone direction in the distribution of the actually measured values andcorresponding modification factors.